Michael and Kevin return to the candy store, but this time they want to purchase nuts. They can't decide among peanuts, cashews, or almonds. They again agree t...

Michael and Kevin return to the candy store, but this time they want to purchase nuts. They can't decide among peanuts, cashews, or almonds. They again agree to create a mix. They bought 2.5 pounds of peanuts for $1.30$dollar per pound, 4 pounds of cashews for $4.50$dollar per pound, and 2 pounds of almonds for $3.75$dollar per pound. Determine the price per pound of the mix.

Back for a party. Leonora bought several pounds, cashes in several pounds, almonds caches cost $8 a pound, and the album is called a $6 the North, about a total of £7 pay the £2048. How many pounds of cashews did she possible before? Pounds of cashews? All right, this is a systems of equations. Problem. All right, let's go back. So the first bit of information is, well, slow us, right? Cashews cost $8 for pound. All right, so we measure things in pounds, so let X be the pounds of cashews. So cashew in pounds and that Why? Sorry. That's a little high. Equal almonds in pounds with Nora bottle of £7. So that means X plus Y has to equal seven. Ah, and paid a total of $48. So we got a total of 48 year. Yeah. How do we work that? Remember, we thought X pounds of cashews in each pound costs a dollar a pound, so it's eight x is the cost of cashews, and it's $6 for pound for almonds. So, six, Why? Since why represents almost right. So we have two equations and two unknowns. We could solve this by elimination. Uh, we're using. I choose elimination because it's easy, right? There's no coefficient on X or Y, or the coefficients are one. Rather. So let's scare riddle. Why would multiply the first equation by negative six. When I do that multiplied by negative six, I'm gonna get negative. Six X minus six y equals negative. 42. Right? So it multiply the first equation by negative six, because I wanted to cancel the six wine. All right, so if I have a negative six in front of the why they will cancel each other, right, I could have chosen X and I would have chosen a different number anyway. I didn't do anything with the second equation was copying how a six foot six wide was 48 and then a combined It's your equations. Eight. X plus Negative. Six. Excuse be positive to X. The negative +61 positive. Six. White canceled each other out. 48 Negative. Who want to be six. Continue to solve for X and I get X equals three and three represents the pounds of cashews. X is, uh, cash. You earn pounds, so my answer is G

According to given cushions, the venue is fixed. So let us support that. Let an physical do phoned off. Guess use. So that means we can say that according to live in you will have nine and less 3.5, maybe floodlit 60. This is a call to 7.5 multiplied with and plus 60. So that means if we calculate this distill commerce nine end and this is 3.5. My deployed with 60 so we can write decides to wonder then on the right side this is 7.5 and 7.5 and multiplied with 60 which is 450 Now. We'll see if this 7.5 and on the left hand side of nine and minus 7.5 it's illegal to for 15 minus, I wondered then. So this is 1.5 and Equality 240. So that means an easy call to wonder. 40 divided by 1.5, which is coming as £160. So does you can say that won the £60 of castles next

In this question will asked how many pounds off my dollar, but all the chocolate mix tribune mixed into pounds off. Who? The limericks 22 results you end up was, ah, $3 bills. So that's expounds on red alert. So anyways, tempt us expand. So you know about the drug causes by vax and 20 because 23 10 plus X So that enough by X plus 20 you close to 30 plus react your Family X to decide that when you do this side, I end up with his two x equal to 10 Ex Yukos to buy so we need £5 off the pad on the Knicks.

When solving this kind of problem, it's a good idea to select your variables and identify what they are. So I'm going to let P equal the number of pounds of peanuts, and I'm going to let be equal the number of pounds of Brazil nuts. And we know the total number of pounds is 480. So that would mean that P plus B equals for 80 and that gives us our first equation. And then we're going to write our second equation based on the costs of the nuts. So we know that peanuts are $3.20 per pound, so the cost of the peanuts would be 3 20 times p, the cost per pound times the number of pounds. And we know that Brazil nuts are $6.40 a pound, so the cost for Brazil nuts would be 6.40 times be the cost per pound times the number of pounds. And we know that the mix costs $5.50 a pound, so the total cost for the mix would be $5.50 times 480. The cost per pound times the number of pounds. This is the part that often trips up students. They don't remember to multiply by 4 80 Okay, so now we have our second equation, and I'm going to solve the system using substitution. So I'm going to take the first equation and isolate WPI. P equals 480 minus B, and I'm going to substitute that into my second equation for the peak. So now we have 3 20 times the quantity for 80 minus B plus 6 40 times be equals. And when you multiply 5.5 by 480 you get 2640. Okay, Now let's distribute the 3.2 and we end up with 15 36 minus 3.2 B plus 6.4 b equals 26 40 and we can subtract 15 36 from both sides. Now we can also combine our life terms. So now we have 3.2. B is equal to 11. 04 Okay, so let's divide both sides by 3.2 and we end up with B equals 345. So that tells us that they were going to be £345 of Brazil nuts. Now we need to also find the number of pounds of peanuts. So remember that the number of pounds of peanuts equals 480 minus the number of pounds of Brazil nuts. So that's going to be 480 minus 3 85 or 3 45 Excuse me, and that gives us 1 35 So we found that they're going to use £135 of peanuts and one hand and £345 of Brazil nuts.