How would I start? Please briefly explain how I would start this process.

Question

My grades on my first 4 math tests were 76, 86, 87, and 90. I want my mean (average) to be at least 87. What would I need to score on test #5 to earn a mean of at least 85? I need to set up and solve an inequality, how would I start?

Answer 1

The mean is calculated by adding the observation values then dividing by the count of observations.

Let x = the minimum score needed on test #5

"mean (average) to be at least 87" creates this inequality:

(76 + 86 + 87 + 90 + x) / 5 ≥ 87 [note: "at least" means "greater than or equal to")

(339 + x) / 5 ≥ 87

339 + x ≥ 435 [multiply by +5 retains the sense of the inequality]

x ≥ 96 [subtract 339 retains the sense of the inequality]

= = = = = = = = ==

"earn a mean of at least 85" creates this inequality:

(76 + 86 + 87 + 90 + x) / 5 ≥ 85 [note: "at least" means "greater than or equal to")

(339 + x) / 5 ≥ 85

339 + x ≥ 425 [multiply by +5 retains the sense of the inequality]

x ≥ 86 [subtract 339 retains the sense of the inequality]

IMPORTANT: While working with an equality may seem to make the solution easier, it does not teach you the rules for working with an inequality. Use this opportunity to learn them now.

Answer 2

you want to start by thinking about the formula for finding averages.

Total Sum

Average = ——————

Number of Things

that could be rewritten as:

Average * Number of Things = Total Sum

A * N = T

you want the average to be: 85

the number of things: 5 (5 test scores in all)

85 * 5 = 425 total point between all five tests

you already have the scores for the first four tests. Add up the scores you already have and subtract that total from 425 to find what you need to get on the fifth and final test in order to average 85.

Answer 3

To get an 87 avg from 5 tests you need 435 points to divide. 435-339=96.