Question

A 100-point test consists of 2-point questions () and 5- point questions (y). There are a total of 44 questions on the test. How many questions of each type are on the test?

system of Equations:

number of 2-point questions:

number of 5-point questions:
​

Answer 1

The number of items for a 2-point question is 40.

The number of items for a 5-point question is 4.

Explanation:

Step 1:

Let x = number of items for a 2-point question

Lex y = number of items for a 5-point question

Step 2: Create a system of equation

x + y = 44 (Equation for the total number of items) -> Equation 1

2x + 5y = 100 (Equation for the total number of points) -> Equation 2

Step 3: Solve the value of x by using the elimination method

Multiply Equation 1 by 5 and subtract it to Equation 2

5(x+y) = 5(44)

5x + 5y = 220

5x + 5y = 220

-(2x + 5y = 100)

Equation: 3x = 120

*Solving for x

x = 120/3

x = 40

Step 4: Substitute the value of x for equation 1

x + y = 44

y = 44 - x

y = 44 - 40

y = 4

Answer:

The number of items for a 2-point question is 40.

The number of items for a 5-point question is 4.