Question

A 100-point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and the short response questions are worth 8points each. A. Write a system of linear equations that represents this situation. B. How many multiple choice questions are on the test? C. How many short response questions are on the test? D. If the teacher changed the test to 15 questions, then how many of each type of question would be on the test?

Answer 1

x = multiple choice

y = short answer

A. 100 = 3x + 8y

x + y = 20

Work for b and c:

x + y = 20

x = 20 - y

100 = 3x + 8y

100 = 3(20 - y) + 8y

100 = 60 - 3y + 8y

100 = 60 + 5y

40 = 5y

8 = y

x + y = 20

x + 8 = 20

x = 12

B. 12 questions

C. 8 questions

Work for D:

x + y = 15

x = 15 - y

100 = 3x + 8y

100 = 3(15 - y) + 8y

100 = 45 - 3y + 8y

100 = 45 + 5y

55 = 5y

11 = y

x + y = 15

x + 11 = 15

x = 4

D. 4 multiple choice and 11 short answer

Answer 2

x = multiple choice
y = short answer
A. 100 = 3x + 8y
x + y = 20

Work for b and c:
x + y = 20
x = 20 - y
100 = 3x + 8y
100 = 3(20 - y) + 8y
100 = 60 - 3y + 8y
100 = 60 + 5y
40 = 5y
8 = y
x + y = 20
x + 8 = 20
x = 12
B. 12 questions
C. 8 questions

Work for D:
x + y = 15
x = 15 - y
100 = 3x + 8y
100 = 3(15 - y) + 8y
100 = 45 - 3y + 8y
100 = 45 + 5y
55 = 5y
11 = y
x + y = 15
x + 11 = 15
x = 4

D. 4 multiple choice and 11 short answer.
Hope this helps!