Question

Your next math test has multiple choice and short answer problems and is worth 111 points. The multiple choice

problems are worth 3 points each and short answer problems are worth 4 points each. There are 32 problems total on
the test. How many of each kind of problem are on the test?
a) Write a system of equations to model the situation
How many of each kind of problem are on the test?

Answer 1

Explanation:

Let M be the number of multiple choice problems and S be the number of short answer problems.

We can set up the following system of equations to represent this situation:

M * 3 + S * 4 = 111

M + S = 32

The first equation represents the total number of points on the test, and the second equation represents the total number of problems on the test.

To solve this system of equations, we can use a method such as graphing, substitution, or elimination.

Using the substitution method, we can solve for one variable in terms of the other and substitute it into the other equation. For example, we can solve the first equation for M:

M = (111 - S * 4) / 3

Then, we can substitute this expression for M into the second equation:

(111 - S * 4) / 3 + S = 32

Solving this equation for S gives us the number of short answer problems:

S = 12

To find the number of multiple choice problems, we can substitute this value for S into the expression for M that we derived earlier:

M = (111 - 12 * 4) / 3

Solving this equation gives us the number of multiple choice problems:

M = 8

Therefore, there are 8 multiple choice problems and 12 short answer problems on the test.