Question

What is the answer? and how?

A math test is worth 100 points. There are a total of 26 questions. There are equation questions that are worth 2 points each and vocabulary questions are 5 points each. Use a system of equations to solve for the number of equation questions and vocabulary questions on the math test.

please show all work.

Answer 1

The math test had 10 equation questions and 16 vocabulary questions.

Explanation:

Given:

Total number of questions in the math test = 26

Total marks of the math test = 100

Points for one equation question = 2

Points for one vocabulary question = 5

To Find:

The number of equation question and vocabulary question = ?

Solution:

Let the number of equation question be x and the number of vocabulary question be y

Then

x+y = 26--------------------------(1)

`x * 2 + y * 5 = 100`----------------------(2)

From equation (1), we get

x = 26-y-----------------------------(3)

Substituting (3) in (2), we get

`(26-y) * 2 + y * 5 = 100`

Now solving the above equation

`(52 -2y) +5y= 100`

`52-2y+5y= 100`

`52 +3y= 100`

`3y= 100-52`

`3y=48`

`y =(48)/(3)`

y=16

Substituting y =16 in eq(3),

x = 26-16

x= 10