Question

A girl has scores of 70​, 73​, 79​, and 72 on her algebra tests.a. Use an inequality to find the score she must make on the final exam to pass the course with an average of 75 or​ higher, given that the final exam counts as three tests.b. Explain the meaning of the answer to part a.

Answer 1

`(294+ x)/(5)\geq 75`

The girl should score more than or equal to 81.

Explanation:

We are given the following in the question:

Girl's score:

70​, 73​, 79​, 72

a) Inequality

Let x be the score of the girl in the final exam.

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`\text{Average score} \geq 75\\\\(\displaystyle\sum x_i)/(5) \geq 75\\\\\Rightarrow (70 + 73 + 79 + 72 + x)/(5)\geq 75\\\Rightarrow (294+ x)/(5)\geq 75\\\\\Rightarrow 294 + x \geq 375\\\Rightarrow x \geq 375-294\\\Rightarrow x \geq 81`

b) Interpretation

Thus, the girl should score more than or equal to 81 on her final test so that she could pass the course with an average of 75 or​ higher.