age problems

Question

arlene and Shaun have a total mass of 105kg. Four times arenas mass is the same as three times Shaun's mass. How heavy is each person?

Answer 1

Lets start by creating some variables to represent the values we are looking for:

 

Let A = Arlene's Mass

Let S = Shaun's Mass

 

Now let's find two different equations to solve for these two variable's using the relationships stated in the problem:

 

We know that

 

A + S = 105 kg

 

And

 

4 x A = 3 x S

 

The next step is to solve for one of the variables in terms of the other.  We'll solve for A in terms of S using the second equation.  Dividing both sides by 4 we get

 

A = 3 x S / 4

 

We will now substitute this result into the first equation to get

 

3 x S / 4 + S = 105

 

Note this is the same as

 

3/4 x S + 4/4 x S = 7 / 4 x S = 105

 

Multiplying both sides of the equation by 4 / 7 we get

 

4 / 7 x 7 / 4 x S = 7 / 4 x 105

 

Which means

 

S = 60

 

Now we can substitute this value for S into our equation for A which gives

 

A = 3 / 4 x S = 3 / 4 x 60 = 45 

 

So we've determined that

 

Arlene is 45kg and Shaun is 60 kg

 

If you want to verify that your solution works you can substitute the values you found back into the original equation

 

A + S = 105 

 

45 + 60 = 105

 

This is a true statement, so the solution works.

 

Good Luck.

 

Cheers

 

Chris