Question

A language arts test is worth 100 points. There is a total of 26 questions. There are spelling word questions thatare worth 2 points each and vocabulary word questions worth 5 points each. How many of each type of questionare there?

Answer 1

Spelling word questions = 10

vocabulary word questions = 16

Explanation:

Let

Spelling word questions = x

vocabulary word questions = y

Total points = 100

Total questions = 26

x + y = 26 (1)

2x + 5y = 100 (2)

From (1)

x = 26 - y

Substitute x = 26 - y into

2x + 5y = 100

2(26 - y) + 5y = 100

52 - 2y + 5y = 100

- 2y + 5y = 100 - 52

3y = 48

y = 48 / 3

= 16

y = 16

Substitute y = 16 into

x + y = 26

x + 16 = 26

x = 26 - 16

= 10

x = 10

Spelling word questions = 10

vocabulary word questions = 16