Question

On a test, Summer got 12 multiple choice and 4 constructed response questions correct. Summer scored 8 points more than Kerry who got 10 multiple choice and 3 constructed response questions correct. Enter an equation that shows how much each multiple choice question (m) and each constructed response question (c) is worth.

Answer 1

`2m + c = 8`

Explanation:

Let m be the marks scored for each correct multiple choice question.

Let c be the marks awarded for a correct constructed response question.

It is given in the question:

Summer's score =
`12m + 4c`

Kerry's score =
`10m + 3c`

Also, Summer's score - 8 = Kerry's score

or we can write, Summer's score = Kerry's score + 8

Putting in the values, we get:

`12m + 4c = 10m + 3c + 8\\= 12m - 10m +4c - 3c = 8\\= 2m + c = 8`

The above equation represents that if two multiple questions are correct and a construction based question is correct, then a total of 8 marks is awarded.

Individual values for m and c cannot be calculated because we need two equations to solve for two variable, m and c.

Answer 2

2m + c = 8

Explanation:

Summer's score = Kerry's score + 8

12m + 4c = 10m + 3c + 8

Combining like terms:

2m + c = 8