Question

Molly took part in a math quiz and scored 55 points on 30 questions. Of the questions, there were 3-point word problems, 2-point calculation questions, and 1-point multiple-choice questions. She answered 5 more 2-point questions than 1-point questions correctly. Find how many of each type of question she answered correctly.

Answer 1

`3\ point\ word = 5`

`2\ point\ word = 15`

`1\ point\ word = 10`

Explanation:

Given

Represent

3-point word with T;

2-point with U and

1-point with V

`U = 5 + V` --- (1)

If total questions is 30, then

`T + U + V = 30` --- (2)

If total points is 55, then

`3T + 2U + V = 55` --- (3)

Substitute 5 + V for U in (2) and (3)

`T + U + V = 30` --- (2)

`T + 5 + V + V = 30`

`T + 5 + 2V = 30`

`T + 2V = 25` ---- (4)

`3T + 2U + V = 55` --- (3)

`3T + 2(5 + V) + V = 55`

`3T + 10 + 2V + V = 55`

`3T + 10 + 3V = 55`

`3T + 3V = 55 - 10`

`3T + 3V = 45`

Divide through by 3

`T + V = 15` ---- (5)

Subtract (5) from (4)

`(T + 2V = 25 )- (T + V = 15)`

`T - T + 2V - V = 25 - 15`

`V = 10`

Recall that:

`U = 5 + V`

`U = 5 + 10`

`U = 15`

Substitute 10 for V in (5)

`T + V = 15`

`T + 10 = 15`

`T = 5`