Question

Anyone help??

ive friends take a maths test
Adam, Brandon, Chen together scored 200 marks
Brandon, Chen and Damion together scored 215
Chen, Damion, Erica together scored 224
Damion and Erica scored more than Chen
The five of them together scored 350 marks

What are their individual scores

Answer 1

`Adam = 60`

`Brandon = 66`

`Chen = 74`

`Damion = 75`

`Erica = 75`

Explanation:

Given

Represent each friend with the first letter of their name

So:

`A + B + C =200`

`B + C + D = 215`

`C + D +E= 224`

`A + B + C + D + E = 350`

`D , E > C`

Substitute:
`A + B + C =200` in
`A + B + C + D + E = 350`

`200 + D + E = 350`

Collect like terms

`D + E = 350-200`

`D + E = 150`

Make D + E the subject in
`C + D +E= 224`

`D + E = 224 - C`

Substitute
`D + E = 224 - C` in
`D + E = 150`

`224 - C = 150`

Collect like terms

`C = 224 - 150`

`C = 74`

Substitute
`C = 74` in
`A + B + C =200` and
`B + C + D = 215`

`A + B + 74 = 200`

`A + B =- 74 + 200`

`A + B =126`

`B + 74 + D = 215`

`B + D = -74 + 215`

`B + D = 141`

So, we have:

`A + B =126`

`B + D = 141`

`D + E = 150`

We have:
`D , E > C`

i.e.

`D , E > 74` and
`D + E = 150`

For
`D , E > 74` and
`D + E = 150` to be true,

`D = E = 75`

i.e.

`75 + 75 = 150`

So, we have:

`D = 75`

`E = 75`

Solve for B

`B + D = 141`

`B + 75 = 141`

`B = 141 - 75`

`B = 66`

Solve for A

`A + B =126`

`A + 66 = 126`

`A = 126 - 66`

`A = 60`