# A test has 25 questions and can earn a student 90 points. True/false questions are worth 3 points, and multiple choice questions are worth 4 points. Write a system equation representative of the...

A test has 25 questions and can earn a student 90 points. True/false questions are worth 3 points, and multiple choice questions are worth 4 points.

Write a system equation representative of the system, stating the number of multiple choice on the test.

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We need to use variables to express the relationship between these different values.

Let X represent the number of True/False questions.

Let Y represent the number of Multiple Choice questions.

We know that X + Y = 25.

We know that 3x + 4Y = 90.

This is enough information for us to solve the problem; we just need to rearrange some of these expressions so that we create a "substitute" value for one of the variables. We'll start by working only with X.

By rearranging the first equation, we can get 25 - Y = X

Now we can substitute this value for X into the second equation:

3(25 - Y) + 4Y = 90

Multiplying this out gives us:

75 - 3Y +4Y = 90

75 + Y = 90

**Y = 15**

Now we can substitute this value into the first equation:

X + 15 = 25

**X = 10**

We can check that this is true:

10 + 15 =25

3(10) + 4(15) = 90

30 + 60 = 90

A test has 25 questions and can earn a student 90 points. True/false questions are worth 3 points, and multiple choice questions are worth 4 points.

Write a system equation representative of the system, stating the number of multiple choice on the test.

x = number of True/False

y = number of Multiple Choice

The total number of questions is 25 so => x + y = 25

There are 90 points possible and T/F = 3 and MC = 4 so => 3x + 4y = 90

We want to solve for the number of MC or y.

x + y = 25 => x = 25 - y

Substitute that into the second equation: 3(25 - y) + 4y = 90

Simplify:

75 - 3y + 4y = 90

y = 15