MHB How to solve these 3 IQ practice questions?

[JDW1]

Hi, I'm JDW, I've got three questions I had in this IQ revision test which I could not complete due to not knowing the method, I'll type questions below, I'm just looking for an explanation on how to answer them, thank you very much :D.

Jack is one and a third times as old as Jill. How old are Jack and Jill if their combined ages total 119?

The average of three numbers is 19. The average of the two of these numbers is 15. What is the third number?

Sid and Mary wish to share out £450,00 in the ratio 3:2 How much will each receive?

 

[SuperSonic4]

Hi, I'm JDW, I've got three questions I had in this IQ revision test which I could not complete due to not knowing the method, I'll type questions below, I'm just looking for an explanation on how to answer them, thank you very much :D.

I find that these word problems become much simpler if you "convert" them to letters and use algebra and write down everything the question tells us.

Jack is one and a third times as old as Jill[/color]. How old are Jack and Jill if their combined ages total 119[/color]?

Let Jack's age be $x$ and Jill's age be $y$.
The question tells us that $x = \frac{4}{3}y$ (the red text) and $x+y = 119$ (the green text)

This is now a straightforward simultaneous equation that can be solved using your favourite method. As a useful check make sure that $x > y$

The average of three numbers is 19. The average of the two of these numbers is 15. What is the third number?

Consider what the average is defined as - the sum of a set of values divided by the amount of values. In symbols $\displaystyle \mu = \frac{a+b+c+...+n}{n}$

Let your three numbers be a, b and c - you should be able to construct simultaneous equations and find the value you want.

Sid and Mary wish to share out £450,00 in the ratio 3:2 How much will each receive?

Ratios are quite simple. Add the "shares" together (3:2) and multiply the initial value by the amount to be shared (450.00). As a check your values should add to £450.00

 

[soroban]

Hello, JDW!

Here's the second one . . .

The average of three numbers is 19.
The average of the two of these numbers is 15.
What is the third number?

Let the three numbers be a,b,c.

Their average is 19: .\frac{a+b+c}{3} \:=\:19 \quad\Rightarrow\quad a + b + c \:=\:57\;\;[1]

The average of two numbers is 15: .\frac{a+b}{2} \:=\:15 \quad\Rightarrow\quad a + b \:=\:30\;\;[2]

Subtract [1] - [2]: .c \:=\:27