An exam worth 145
points contains 50
questions. Some of the
questions are worth two
points and some are worth
five points. How many two-
point questions are on the
test? How many five-point
questions are on the test?
Write a linear system of
equations that can be used
to solve this problem.
number of 2 pointers --- x
number of 3 pointers ---- y
x + y = 50 or y = 50-x
2x + 3y = 145
use substitution:
2x + 3y = 145
2x + 3(50-x) = 145
2x + 150 - 3x = 145
-x = -5
x = 5
so 5 two-pointers and 45 three-pointers
check:
5+45 = 50, the count checks
2(5) + 3(45) = 10 + 135 = 145 , the total value checks
All is good!
Let's assume that the number of two-point questions on the test is represented by variable 'x', and the number of five-point questions is represented by variable 'y'.
We can set up the following linear system of equations to solve the problem:
1. The total number of questions on the test:
x + y = 50
2. The total point value of the questions on the test:
2x + 5y = 145
These two equations represent the total number of questions and the total point value respectively. Solving this system of equations will give us the value of 'x' (the number of two-point questions) and 'y' (the number of five-point questions).
To solve this problem, let's denote the number of two-point questions as "x" and the number of five-point questions as "y."
We know that the exam contains 50 questions, so the sum of the number of two-point questions and the number of five-point questions equals 50:
x + y = 50
Next, we need to consider the total point value of the exam. We know that each two-point question contributes 2 points and each five-point question contributes 5 points. Therefore, the total point value of the exam can be expressed as:
2x + 5y = 145
So, we have the following linear system of equations:
x + y = 50
2x + 5y = 145
By solving this system of equations, we can find the values of "x" and "y," which will tell us the number of two-point questions and five-point questions on the test.