Question

you are taking a test worth 130 points. There are a total of 50 five-point and two-point questions. How many five-point questions are there on the test?

Answer 1

10 five-point questions and 40 two-point questions

Explanation:

Let x represent the total number of five-point questions and y represent the total number of two-point questions.

Equation 1: 5x+2y=130

Equation 2: x+y=50

Multiplying Equation 2 by 2: 2x+2y=100 (Equation 3)

(Equation 1) - (Equation 3): 3x=30

x=10

Substituting x=10 into x+y=50: 10+y=50

y=40

Therefore, there are 10 five-point questions and 40 two-point questions.

Check

Substituting x=10 and y=40 into Equation 1:

LHS=5x+2y=5(10)+2(40)=50+80=130

RHS=130

LHS=RHS

Substituting x=10 and y=40 into Equation 2:

LHS=x+y=10+40=50

RHS=50

LHS=RHS

Since in both cases the left-hand side is equal to the right-hand side, the answer is correct.

(LHS: left-hand side, RHS: right-hand side)