Question

lisa has scored 72, 65, 87, 60, and 59 on her previous five tests. what score does she need on her next test so that her average (mean) is 72?

Explanation:

Step1: Recall the mean formula

The mean (average) of a set of numbers is the sum of the numbers divided by the count of the numbers. Let the score on the next test be \( x \). After the next test, there will be \( 5 + 1=6 \) tests. The mean of the 6 tests should be 72. So the formula for the mean is \( \frac{\text{Sum of all scores}}{\text{Number of tests}} = 72 \).

Step2: Calculate the sum of previous scores

First, find the sum of the previous five test scores: \( 72 + 65+87 + 60+59 \). Let's calculate that: \( 72+65 = 137 \), \( 137+87 = 224 \), \( 224+60 = 284 \), \( 284+59 = 343 \).

Step3: Set up the equation for the mean

The sum of all six scores will be \( 343 + x \), and the number of scores is 6. So we have the equation \( \frac{343 + x}{6}=72 \).

Step4: Solve the equation for \( x \)

Multiply both sides of the equation by 6: \( 343 + x=72\times6 \). Calculate \( 72\times6 = 432 \). Then subtract 343 from both sides: \( x = 432 - 343 \).

Step5: Calculate the value of \( x \)

\( 432-343 = 89 \).

Answer:

89