Question

A student scored 75 and 92 on some tests. Write and solve an inequality to find values for the third test score that would give her an average between 80 and 90 inclusive

Answer 1

Mo is selling key chains as a fundraiser. If their goal is to raise at least $135, how many key chains must they sell at $1.50 each to meet that goal?

Answer 2

Let's call the third test score "x".

To find the average of the three test scores, we need to add up the scores and divide by 3.

The average between 80 and 90 inclusive is between 80 and 90, so we can write the inequality as:

80 ≤ (75 + 92 + x)/3 ≤ 90

Now let's solve for x:

80 ≤ (75 + 92 + x)/3 ≤ 90

Multiply both sides of the inequality by 3:

240 ≤ 75 + 92 + x ≤ 270

Combine like terms:

240 ≤ 167 + x ≤ 270

Subtract 167 from all sides:

240 - 167 ≤ 167 - 167 + x ≤ 270 - 167

73 ≤ x ≤ 103

So the values for the third test score that would give her an average between 80 and 90 inclusive are any values between 73 and 103.

Answer 3

Let's denote the number of key chains Mo must sell as "x".

Since each key chain is sold for $1.50, the total amount of money raised by selling "x" key chains can be calculated as 1.50x dollars.

According to the problem, the goal is to raise at least $135. Therefore, we can write the inequality:

1.50x ≥ 135

To find the minimum number of key chains that Mo must sell, we need to solve this inequality for "x".

Divide both sides of the inequality by 1.50:

x ≥ 135 / 1.50

Simplifying the right side of the inequality:

x ≥ 90

Thus, Mo must sell at least 90 key chains in order to meet their goal of raising $135 or more.