5

Pre-Algebra Extra Credit Solve Multi-Step EquationsAGES Mel is 3 years older than Rahfat and Aurelio is twice as old as Mel. The sum of their ages is 57. How old is...

Question

Pre-Algebra Extra Credit Solve Multi-Step EquationsAGES Mel is 3 years older than Rahfat and Aurelio is twice as old as Mel. The sum of their ages is 57. How old is Mel?

Pre-Algebra Extra Credit Solve Multi-Step Equations AGES Mel is 3 years older than Rahfat and Aurelio is twice as old as Mel. The sum of their ages is 57. How old is Mel?



Answers

Solve each problem. Kevin is three times as old as Bob. Three years ago the sum of their ages was 22 yr. How old is each now? (Hint: Write an expression first for the age of cach now and then for the age of each three years ago.)

So we for this problem were given that Lha Wana is exactly five years older than her brother. So will represent her brothers age with just acts Marijuana's Will X plus five. Now we're also given that the sum of their ages is equal to 37. So this is one age. This is the others. They should some to 37 so we have X plus five puts. X is equal to 37. No, we'll subtract five from both sides because we're solving for X, so that will go away. On the left hand side, 37 minus five is 32 and we have to excess leftover will just combine like terms on the left hand side. So we have two X equal to 30 to divide both sides by two, and we have X is equal to 16. Now. Remember, X was representing her brothers age, not hers. So if we want to find Rwanda's age, we need to take X plus five. So 16 plus five is equal to 21 and this is our answer

We know that Kevin is three times as old as Bob, so we will represent Bob's age as X and Kevin. Being three times older will represent as three x. The information were given toe work with, though, was three years ago. So dealing with three years ago, Bob would have been X minus three years old, and Kevin would have been three x minus three years old. That's three years ago, and it said, um, the sum of their ages was 22. So the X minus three plus the three x minus three has to equal 22. Combining like terms will have four. X minus six is equal to 22. Add six to both sides. We have four X equals Add six gives US 28. Divide by four. X equals seven. So Bob's age is seven and Kevin, who is three times older, would be 21

Problems are always so much fun, but the freak people out a little. So don't let don't let it scare you, Okay? We have a situation where we have a student named Chun Wai, and we know that his mother is eight more than twice his age. So his mom her age is twice more. So I'll just go ahead and say what two times Use it dot since we'll end up with the next year. So two times ate more than his son's age. Okay, so I'm gonna go ahead before going further and set up some variables. So let's say C is to analyze age and we'll say that M is his mom's age. Okay, so if I know that her age is eight more than twice his age, ate more than twice his age. I'm gonna do twice his age, so to see, plus eight. And that's her age. So so far, I have see as the sun's age to see, plus eight as the mom's age, and the last piece is the dad's age. He is three years older than the mother, so I'm gonna go ahead and set up one more variable, which is Dad and he's three years older than Mom. So Mom is M So I'm gonna go ahead and make Dad M plus three. Okay, so I have three equations here. I have the dad equation. The mom equation and internalized equation is just a C because that's his age. And I'm told that the sum the total sum of their living years is 94. So that means C plus M plus D is 94. The number of years June wise lived the number of years his mom has lived in the number of years his dad has lived. So I don't want to add it like this. I have three variables. What I want to do is take advantage of the fact that I can represent things in different ways. So so far I have C is See, I have rewritten M as this, so I'm gonna use that for mom's age. And I want to do a similar thing for dad's age to keep just one variable. So let's go back here, too. Mom's age plus three equals Dad's age will remember that mom's age is this. So I'm gonna go ahead and insert that right there and rewrite dads to B to C plus eight plus three. So that means to seed plus 11 his dad's age. And I'm gonna stick that right there. So to see, plus 11. Okay, let's add all the like terms so that we can simplify. I have to see to see and to see. So that's five C and then I have eight and 11. That's 19 equals 94. Well, go ahead and solved by subtracting 19. And that's 85. And then we're gonna divide by five. And so we get that sea tuna y equals 15. He is 15 years old. Okay, so that's great. Except they want to know everyone's age. So I have his age as 15. I also need to find mom's age. Okay, so I'm gonna go back to where I wrote this equivalent expression, and she is to see so two times 15 plus eight. She's 38. And then remember that dad right here he is her age plus three. So he's gonna be 41. So, you know, I is 15. His mom is 38 Dad is 41

All right, So for this question, we have the following information between Mike and Join. We know that Mike is five years older than join, and that in 10 years does some of their ages is going to be 57 on. We're trying to solve their current age. So this is we're gonna used the same principles that we used before where we're going to try to be selling for to unknown variables and these they're gonna be in your equations. And there is to the power of one. We're gonna use the fact that addition and subtraction will under each other, and multiplication and division will under each other too. So we have Mike and join. Mike is five years older than join. So you know that makes current age and just write it down Nights Current age is equal to Joan's plus five because he's five years older than Joanne. And we know that in 10 years, the some off with their agents is gonna be 57. So we have Mike. Plus, Joanne is equal to 57. But it's important to note that this is in 10 years time, so they're both going to be and years old, you're gonna have time to each of them and now and simply substitute. So we have two equations basically, Um, but we're just going to substitute this, Um, because J plus five value here into this m they're going to replace them with J Plus five because we know that em is equal to this. So we're gonna have J plus five so again, which is replaced. Simplified. Um, okay. Plus 10 again is equal to 37. And now we can solve this with our regular rules, simplify, rearrange and then isolate J. So we want we want to get J by itself at the end. So we're gonna have J plus J is just too. Jay. Yeah, those five plus 10 plus 10. So that's 25. We have 25 quick to 57 and we want to get TJ by itself. So we're gonna attract both sides of the equation by 25 five kill. So now we have okay on, then 25 minutes. 25. It's just your old And then we have 57 minus 25 which is just 32. If no, we can simplify this even further we're gonna isolate J, letting both sides of the equation by two. So we're gonna have to get a better way to. We have that k by itself because two divided by two is just one. J J is equal to 32 divided by two. That's simply 16. So we know that case age is 16. We're gonna plug in this value into the original equation to find mix age. So now we have Mike is able to J, which is 16 type. Come with eight is equal to 21. I don't think the ones age 16 mixed age is 21.


Similar Solved Questions

5 answers
A disc of 2 kg mass is located on an ice rink between two springs with constants of 8 N m separated by a distance of 10 meters. The disc starts from the middle point between the two springs towards the right one at a speed of 1.5 m / $, compresses it and then goes to the spring on the left:to Determine the time to complete a cycle for the diskb. Determine the maximum displacement of the spring when it is compressed due to arrival of the disc.
A disc of 2 kg mass is located on an ice rink between two springs with constants of 8 N m separated by a distance of 10 meters. The disc starts from the middle point between the two springs towards the right one at a speed of 1.5 m / $, compresses it and then goes to the spring on the left: to Deter...
5 answers
Consider the matrixA= [' 7]Using the standard formula for the inverse ofa 2 x 2 matrix, calculate the inverse matrix exactly: Calculate the condition number K IA, 'IA,I: How well-conditioned or ill-conditioned is this matrix?(iii) Use the inverse to compute the exact solutions to Anx; = b; i = 1.2,for b1andDiscuss the results, paying particular attention to the behaviour of the solutions as
Consider the matrix A= [' 7] Using the standard formula for the inverse ofa 2 x 2 matrix, calculate the inverse matrix exactly: Calculate the condition number K IA, 'IA,I: How well-conditioned or ill-conditioned is this matrix? (iii) Use the inverse to compute the exact solutions to Anx; =...
5 answers
Silver tarnishes (reacts) In alr In the presence of Hzs. The balanced reaction equation Is: 4Ag(s) 2H2S(g) Oz(g) 2Ag2S(s) 2H20() MM (glmol) 107.9 34.08 32.0 247.8 Moles MassiMolar mass With correct Sig Figs, calculate the theoretical yield of silver sulfide if the reaction uses 45.329 of silver: 247.88123.9852.04g 104.1g
Silver tarnishes (reacts) In alr In the presence of Hzs. The balanced reaction equation Is: 4Ag(s) 2H2S(g) Oz(g) 2Ag2S(s) 2H20() MM (glmol) 107.9 34.08 32.0 247.8 Moles MassiMolar mass With correct Sig Figs, calculate the theoretical yield of silver sulfide if the reaction uses 45.329 of silver: 247...
5 answers
UecrIxbo dbuele uchoimanjom waruni OthncdonCinnot Octemmlrc bracdelvrnIfonutlonTh? Dotarce EfTrytcn major @Lk$ Ina h cmanUulaa Whur#- [hc stunduddeviatio ! ol thc datarce bctueenmalo
Uecr Ixbo dbuele uchoimanjom waruni Othncdon Cinnot Octemmlrc bracd elvrnIfonutlon Th? Dotarce EfTrytcn major @Lk$ Ina h cman Uulaa Whur#- [hc stunduddeviatio ! ol thc datarce bctueenmalo...
5 answers
Ynt2 - 3y.-1 + 3y. = 1
Ynt2 - 3y.-1 + 3y. = 1...
2 answers
Describe the relationship between the initial horizontal velocity of the ball bearing and its horizontal displacement Use data from your data table and graph to support your claim.Answer using 3 to 4 complete sentences:YOUR RESPONSE We can conclude that initial velocity Vix of the ball bearing is directly proportional to average horizontal displacement 4 x covered by the ball bearing: The proportionalit constant is time {=0.403. Therefore; we can write 4 Vi*f x
Describe the relationship between the initial horizontal velocity of the ball bearing and its horizontal displacement Use data from your data table and graph to support your claim. Answer using 3 to 4 complete sentences: YOUR RESPONSE We can conclude that initial velocity Vix of the ball bearing is ...
5 answers
21 + 2y, =I+ 3y;(15 pts) Find the solution of the initial value problem I(0) = 1, y(0) = -1.
21 + 2y, =I+ 3y; (15 pts) Find the solution of the initial value problem I(0) = 1, y(0) = -1....
5 answers
QUESTION2e2*cos(eZx) Find the integral dx. sinle2x)In(2e2rcosleZn))+c In(sin(e2x))+c 2*sinle 21) cosle2r) +Csinle2r)+cQuESTion 2Convert the number 2 = ~ 3 + 4 to polar form 0 2=522.214 0 2=52-1.333 0 25521.333 0 2=52-0.927
QUESTION 2e2*cos(eZx) Find the integral dx. sinle2x) In(2e2rcosleZn))+c In(sin(e2x))+c 2*sinle 21) cosle2r) +C sinle2r)+c QuESTion 2 Convert the number 2 = ~ 3 + 4 to polar form 0 2=522.214 0 2=52-1.333 0 25521.333 0 2=52-0.927...
5 answers
Unsinn the shed I0 € Tne ballbon then taken outside; ed with 29,5 Inelda Mep shed, tcm peraturd Hn atctle wcathot bhlloon heium qas Caiculatethe MHlt Volnte Wballoon Wner {emotraturg tre Dalcon ELoys consum eecLly Idund Your Anexei vgnlticent d qits. olmay Ml nna t7te Ordeeute
Unsinn the shed I0 € Tne ballbon then taken outside; ed with 29,5 Inelda Mep shed, tcm peraturd Hn atctle wcathot bhlloon heium qas Caiculatethe MHlt Volnte Wballoon Wner {emotraturg tre Dalcon ELoys consum eecLly Idund Your Anexei vgnlticent d qits. olmay Ml nna t7te Ordeeute...
5 answers
A hotel has 10 small 10-square meter rooms, 30 medium sized 16square meter rooms and 20 large 25 square meter rooms. Calculatethe average room size.
A hotel has 10 small 10-square meter rooms, 30 medium sized 16 square meter rooms and 20 large 25 square meter rooms. Calculate the average room size....
5 answers
Answer each of the following questions: (a) Ka for HNO2 is 4.6 x 10-4 . What is the Kb for its conjugatebase ?(b) Calculate the pH of 0.1 M of HNO2 solution above.
Answer each of the following questions: (a) Ka for HNO2 is 4.6 x 10-4 . What is the Kb for its conjugate base ? (b) Calculate the pH of 0.1 M of HNO2 solution above....
5 answers
The yield of strawberty plants _ depends on the amount of fertilizer fed to the plants. Agricultural research shows that an acn 0 strawberry plants will yield 480 pounds of strawberries when 60 cubic feet of fcrtilizer are applied If 80 cubic of fcet of fertilizer are applicd, the yield will be 640 pounds of strawberries; Use linenr interpxlation to estimate the yicld if 73 cubic fcet of fertilizer are appliedSelect an answer
The yield of strawberty plants _ depends on the amount of fertilizer fed to the plants. Agricultural research shows that an acn 0 strawberry plants will yield 480 pounds of strawberries when 60 cubic feet of fcrtilizer are applied If 80 cubic of fcet of fertilizer are applicd, the yield will be 640 ...
5 answers
Question 13In sereral neurological diseases; axons lose their ingulating myelin sheath What is the consequence ofthis loss? Action potential transmission speeds Up Nerve cells lose to mucn heat Actions potential transmission slowis down Nerve cells retain to much heat
Question 13 In sereral neurological diseases; axons lose their ingulating myelin sheath What is the consequence ofthis loss? Action potential transmission speeds Up Nerve cells lose to mucn heat Actions potential transmission slowis down Nerve cells retain to much heat...
5 answers
Use Ihe following Informallon answor the next Titrallon " quostion Data12. Which row below shown identifies above? the titrant- and (he sample for Ihe utration The data statement above is best completed by the answers in Tow: Row Titrant Sample Ca(OH)(aq) HzSO-(aq) HCI(aq) NazCOs(aq) NazCOz(aq) HCI(aq) HCI(aq) Ca(OH)z(aq)
Use Ihe following Informallon answor the next Titrallon " quostion Data 12. Which row below shown identifies above? the titrant- and (he sample for Ihe utration The data statement above is best completed by the answers in Tow: Row Titrant Sample Ca(OH)(aq) HzSO-(aq) HCI(aq) NazCOs(aq) NazCOz(aq...

-- 0.026122--