Question

A math test is made up of 5-point questions and 10-point questions. There are 24 questions on the test. The total number of possible points is 150 points. Write a system of linear equations to represent the problem. Use f for 5-point questions and t for 10-point questions. Find the intercepts of the graph of each equation you wrote in part a. State your answers in complete sentences. Use the intercepts from part b. to graph the system of linear equations. Label each axis to show what it represents. Label each line. What is the total value of all the 10-point questions on the test? Explain.

Answer 1

In accordance with the instructions above:
Let f = the number of 5 point questions
Let t = the number of 10 point questions
Given: f + t = 24
Given total score = 150 points
Solution:
f=24-t substitute this in the equation for total points.
5(24-t) + 10t = 150
120-5t +10t = 150
5t =30
t=6
f=24-6=18
6 ten point questions
18 5 point questions
6 +18 =24
60 + 90 = 150