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On his first 3 exams, Bob scored 79, 54, and 61. What score must Bob have on the fourth exam to come to an average of 71 for all of the four exams?

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Question:

A
90

explanation

Let x represent Bob’s score on his fourth exam.

In this case, the unknown is the score on Bob’s fourth exam. To find the average of four exam scores, sum the four scores, then divide by 4.

\((79+61+54+x) \div 4=71\)

This last result can be simplified by summing the three known exam scores. \(\frac{\mathrm{194+x} }{\mathrm{4}} =71\)

To isolate x, multiply both sides of the equation by 4.

\(\frac{\mathrm{194+x} }{\mathrm{4}} =71\)

\(4(\frac{\mathrm{194+x} }{\mathrm{4}}) = 4 \times 71\)

\(x+194=284\)

We need to isolate x once again, so we subtract 194 from both sides of the equation.

\(x + 194 − 194 = 284 − 194\)

\(x = 90\)

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