Your math test scores are 68, 78, 90, and 91. What is the lowest score you

Your math test scores are 68, 78, 90, and 91.
What is the lowest score you can earn on the next test and still achieve an average of at least 85?
Getting an Answer Solve your inequality to find the lowest score you can earn on the next test and still achieve an average of at least 85.
What score do you need to earn?

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Dona Hall
Step 1
$$\displaystyle{\frac{{{68}+{78}+{90}+{91}+{x}}}{{{5}}}}\geq{85}$$
$$\displaystyle{68}+{78}+{90}+{91}\geq{5}\times{85}$$
$$\displaystyle{327}+{x}\geq{425}$$
$$\displaystyle{x}\geq{98}$$
So, the minimum score required to have an average of at lest 85 is 98.
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Twereen
Step 1
Assuming the grade won't be rounded up or down to the nearest whole point, our cumalitive points would have to add up to 425.
We can find this by multiplying the average we want (85%) by the total possible points (500).
$$\displaystyle{0.85}\times{500}={425}$$
We then create this equation where x-fifth test score.
$$\displaystyle{68}+{78}+{90}+{91}+{x}={85}$$
Then solve for x.
$$\displaystyle{68}+{78}+{90}+{91}+{x}={425}$$
$$\displaystyle{327}+{x}={425}$$
$$\displaystyle{x}={98}$$
Thus, the minimum score on the last test would have to be a 98 to achieve an average of 85.
However, if the final grade is rounded, the new average we have to achieve is actually an 84.5%. Just follow the same steps as before:
$$\displaystyle{0.845}\times{500}={422.5}$$
$$\displaystyle{68}+{78}+{90}+{91}+{x}={422.5}$$
$$\displaystyle{327}+{x}={422.5}$$
$$\displaystyle{x}={95.5}$$
So in that scenario, you would be able to squeeze by with a 95.5 on that test.
user_27qwe

Step 1

Math test scores are 68, 78, 90 and 91

Average of five scores have to be at least 85.

Step 2

Let the unknown score be x

$$\text{Average}=\frac{\text{Total marks}}{\text{number of counts}}$$

For at least, one have to use $$\geq$$

Therefore

$$\frac{68+78+90+91+x}{5}\geq85$$

$$327+x\geq425$$

$$x\geq98$$

So the lowest score is 98.