Question

Rachel has 60 scones. She sells them to Robbie, Cameron, Louis, Tom and

Charlie in that order. Each customer buys more scones than the last and the
increase is the same number in each case. Robbie and Cameron’s combined
total number of scones is three sevenths of the total of Louis, Tom and Charlie.

How many scones does each boy buy?

Answer 1

We can start by writing all that we know about the problem. Let us write down how many scones each boy has:

`R_(o) : x`

`C_(a) : x+k`

`L_(o) : x+2k`

`T_(o) : x+3k`

`C_(h) : x+4k`
Note that k is the increase, we know it's a constant. This is not a system of equations, please keep that in mind. We will use rest of the information given to build the system. We have two variables x (the number of cookies the first boy bought) and k( the increase), that means we need to have two equations to solve this problem.
We know that total amount of scones is 60, so we can use that information to build our first equation. We sum all of the scones and we get 60.

`R_(o)+C_(a)+L_(o)+T_(o)+C_(h)=60`

`5x+10k=60`
We know that Robbie and Cameron combined have 3/7 of Louis, Tom and Charlie combined. We can use this information to build our second equation.

`R_o+C_a= (3)/(7) (L_o+T_o+C_h)`

`2x+k= (3)/(7) (x+2k+x+3k+x+4k)`

`2x+k= (3)/(7) (3x+9k)`

`14x+7k=9x+27k`

`5x=20k`

`x=4k`
Now this piece of information alows us to solve the first equation that we made and this will solve our problem. We simply plug in x=4k into 5x+10k=60.

`5(4k)+10k=60`

`30k=60`

`k=2`
Now we can plug this information into the same equation 5x+10k=60 and get x.

`5x+10(2)=60`

`5x=40`

`x=8`
And that's it. Now we can write out how many cookies each boy has bought.

`R_(o) : x=8`

`C_(a) : x+k=10`

`L_(o) : x+2k=12`

`T_(o) : x+3k=14`

`C_(h) : x+4k=16`
If you add them all up you get 60.