Question

Your math teacher is planning a test for you. The test will have 30 questions. Some of the questions will be worth 3 points, and the others will be worth 4 points. There will be a total of 100 points on the test. How many 3 -point questions and how many 4 -point questions will be on the test?a. Identify the problem:b. Let the number of 3 -point questions =x and the number of 4 -point questions =y . Write the two equations for the system.c. Use subsititution to solve for y in the first equation.d. Substitute the value for y into the second equation to solve for x.e. There will be ___ 3-point questions and____ 4 -point questions.f. Check your solution by substituting the values into both equations.

Answer 1

Step-by-step explanation:

(a)The problem is to find out how many 3 -point questions and how many 4 -point questions will be on the test.

(b)

Let the number of 3-point questions =x

Let the number of 4 -point questions =y

The test will have 30 questions, therefore:

`x+y=30`

Since the test will have a total of 100 points, we have:

`3x+4y=100`

(c)From the first equation: x=30-y

Substitute into the second.