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A class consists of a number of boys whose ages are in arithmetical progressions, the common difference being four months. If the youngest boy of the class be only ...

Question

A class consists of a number of boys whose ages are in arithmetical progressions, the common difference being four months. If the youngest boy of the class be only eingt years old and the sum of the ages of all the boys in the class be 168 years, find the number of boys and the age of the oldest in the class.

A class consists of a number of boys whose ages are in arithmetical progressions, the common difference being four months. If the youngest boy of the class be only eingt years old and the sum of the ages of all the boys in the class be 168 years, find the number of boys and the age of the oldest in the class.



Answers

In Exercises 79 and 80, three siblings are of three different ages. The oldest is twice the age of the middle sibling, and the middle sibling is six years older than one-half the age of the youngest.

(a)
Write a composite function that gives the oldest sibling's age in terms of the youngest. Explain how you arrived at your answer.
(b)
If the oldest sibling is 16 years old, find the ages of the other two siblings.

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.

Okay, So we want to relate the number of girls to the number of boys and say that G is the number of girls abuse the number of boys. Um, and we know that four less than anything is going to really be that anything minus four, because we want four fewer of them. So in this case, we can say that G the number of girls is going to equal anything. Or in this case, number boys minus four. Because we want four less. Boy. So, boys, the total number of boys minus four is going to be the total number of girls.

These numbers represent the ages in months of some three year olds in a swim class, we want to find the median, which is the middle value, and so we start by putting the numbers in order from least to greatest. We have 36 38 40 41 42 and 45. It's a good idea to check him off is you go and make sure that you don't miss anything. So we have six numbers, and whenever we have an even number of values, we need to average the middle to There's no one middle number, but we can average the middle to to get the median. So the average or the mean is what you get if you add the middle two numbers together and divide by two, and that gives us 40.5. So that tells us the median age of the Children in the swim class is 40.5 months

Okay, So in this problem, we're told that there's a school club that has 16 girls. We're also told a number of girls in this club is four more than two times the number of boys. And then we're asked to find out the number of boys. Well, the unknown in this equation is the number of boys. So let's represent that with a variable. Let's use B for boys. Now let's try by presenting this piece of information using math. So we know the number of girls, which is 16 is equal to four more than two times the number of boys. So four more is four plus two times the number of boys you know the number of voices be so two times. Number of boys is two times be. Now we can sell this equation by subtracting for from both sides. To get 12 is equal to to be. And then we divide both sides by two to get B equal six. And so from this we can tell the number of boys six


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