A100-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?

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!

Given:

Consider the complete question is "Patty and carl went to the movie. Patty bought two tickets for 7.35 each. Carl bought two buckets of popcorn at 5.60 each. How much more money did patty spend than carl?".

To find:

How much more money did patty spend than carl?

Solution:

We have,

Price of 1 ticket = 7.35

Price of 1 bucket of popcorn = 5.60

Using the given information, we get

Price of 2 ticket = 2(7.35) = 14.70

Price of 2 bucket of popcorn = 2(5.60) = 11.20

Now, difference between the amounts spend by patty and carl is

Therefore, patty spend 3.50 more than carl.