Question

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.\

Answer 1

First rearrange x+y=24 to x=24-y this makes 3x+5y=100 become :

3(24-y)+5y=100

Second use the distributive property to get:

72-3y+5y=100

Then subtract 3 from 3y and 3 from 5x to get:

72+2y=100

Subtract 72 from 100 to make:

2y=28

y=14 and x=10

So there are 10 3-point questions and 14 5-point questions. Making the correct answer to be B) The test contains 10 three-point questions and 14 five-point questions.

Answer 2

here we are given the two equations:

x + y = 24

x=24-y............(1)

3x + 5y = 100..................(2)

plugging the value of x from (1) in (2)

3(24-y) +5y =100

72 -3y +5y =100

2y=100-72

2y=28

y=14

plugging value of y in equation (1)

x=24-y =24-14=10

x=10 and y=14

Answer : The test contains 10 three-point questions and 14 five-point questions.