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

Answer:

$3\ point\ word = 5$

$2\ point\ word = 15$

$1\ point\ word = 10$

Step-by-step 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)

$T + V = 15$

$T + 10 = 15$

$T = 5$