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Boy is 10 years younger than his sister: If he is (x 17) years old; how long will it take for his sister to be x lyears old?a. 7 yearsb. 17 yearsc. 27 yearsd. 10 ye...

Question

Boy is 10 years younger than his sister: If he is (x 17) years old; how long will it take for his sister to be x lyears old?a. 7 yearsb. 17 yearsc. 27 yearsd. 10 years

boy is 10 years younger than his sister: If he is (x 17) years old; how long will it take for his sister to be x lyears old? a. 7 years b. 17 years c. 27 years d. 10 years



Answers

Maria's kids. The sum of the squares of the ages of Maria's two kids is $289 .$ If the boy is seven years older than the girl, then what are their ages?

All right. Um, problem 16. This time we're converting these months and years, right? So for this one, we're converting months, Two years, and we know that one year is equals to 12 months. Okay, so we're converting 100 to we go 100 to once, and since we are converting to a larger unit, we need to divide that by 12. Okay, so let's go for our loan division, we got 102 divided by 12. Okay, so if you go over the multiples of dolls, um, you'll get that one, um, 12 times eight, 12 times eight would be 96 right? Sometimes it would be 96 12 times nine would be 108. So we need to go, um, to to the multiples of 12 and find the closest number we could get to. And I got it from that. Right. And eight times to all this 96 you could confirm that by just writing all the multiples of 12 until you get to 96 108. So, um, you subtract 96 from 100 to write, so we borrow one from 10. 12 minus. This becomes the nine right away. 12 minus six is six. So now we have a remainder. So I want to add a zero right here as a placeholder, and I want to bring down that zero to make it 60. But before that, I want to copy this decimal point to our answer. Okay, So how many tools fit in 60? You got slides? Okay, $5. 12 would be 60. And that gives us our answer. 8.5. He's going five years.

Okay. We use these pieces of information in the last problem and we found that we could express the oldest Z as a function of the middle. Why? By writing it as e equals two. Why? And we found that we could express the middle. Why, as a function of the youngest X as 1/2 X plus six. So, based on that, we were able to find Z of why, by composing Z and why So Z was the outside function and why was the inside function and that gave us two times a quantity 1/2 X plus six. So we found that Z is equal to X plus 12. Okay, so in this problem, suppose we want to know x as a function of Z rather than Z as a function of X. So that's what we have here From the last problem we have Z as a function of X. All we need to do to get X as a function of Z is isolate X. So let's subtract 12 from both sides and we get X equals e minus 12. Easy is that And then for part B, we are told that the youngest is two years old, so X equals two. Let's go ahead and find the ages of the others. So if X equals two, we know that why, as a function of X is 1/2 of X plus six so 1/2 of to plus six would be seven. So the middle one is seven years old, and we also know that Z as a function of why. So the oldest as a function of the middle is two times the middle two times seven, so the oldest is 14.

All right. Suppose that we established variables X, y and Z for the ages of the siblings. X is the age of the youngest twice the age of the middle and Z is the age of the oldest. So then we can write a couple of functions based on what we're told in the problem. We're told the oldest is twice the age of the middle. And so we could say Z the oldest, as a function of why is two times y Z is two times why We also know that the middle is six years older than 1/2 the age of the youngest. So the middle why, as a function of the youngest X is six more than 1/2 of X. Okay, so what we want to do for part a is right the composite composite function or composite function giving the oldest as a function of the youngest. So we want Z of X. So what we're going to do is we're going to let why be the inside function and we're going to substituted into Z. So we're going to find Z of why of X. So the subsidence, or why substituted into Z gives us two times a quantity 1/2 X plus six and that gives us X Plus 12 and then for Part B. We're told that the oldest is 16 years old, so Z equals 16. So let's go ahead and find the ages of the other two. We know that Z, as a function of why is two times why. So we know that 16 is two times why. So that tells us that the middle one is eight and we also know from a working part a That Z is X plus 12. So 16 is X plus 12. So X is four, so the youngest one is for.

All right. So here it asked how old? Um, what was the age of our older students? And so when we look at that chart, we've got bins under 12 to 13. 14 to 15 and 16 to 17. And then at the end, we have a bit of 18 to 19. And since there are kids in that van are older students are going to be 18 to 19 years old.


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