Question

A math test with 42 questions is worth 186 points there are multiple choice questions that are worth two points and short answer questions that are worth seven points how many types of each question are there?

Answer 1

There are 21.6, 2 points questions and 20.4, 7 points questions.

Explanation:

So let start by making a system of equation.

So the system of equation for this problem can be expressed as:

`2x+7y = 186`
`x+y=42`

Where,
- x = number of two points question
- y= number of seven points question

Now to solve for the system of equation, there are ways we can do it but let use substitution method. So we can easily make the second system of equation in slope form which would be easy to plug into the first system of equation.

`x+y=42`
`y=-x+42` - Subtract x from both sides.

So now we can plug it back into the first equation.

`2x+7(-x+42)=186`
`2x-7x+294=186` - Distribute the 7 to the term inside parentheses
`-5x+294=186` - Combining like terms
`-5x=-108` - Subtracted 294 from both sides
`x=21.6` - Divide both sides by -5 which result in a positive number

Now, we can plug it back into the equation `y=-x+42`

`y=-(21.6)+42`
`y=-21+42` - Distribute the negative sign
`y=20.4` - Combine like terms