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Ballparking: Overview

$$\displaystyle\frac{0.4x+1.05}{7.05-0.05x}=8.4$$ Which of the following is closest to the value of $$x$$?
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Don't be stumped by ugly numbers. Ballpark instead. Use approximations that allow you to solve the problem faster, more comfortably, and correctly.

For instance,

Use 1 instead of 1.05

Use 7 instead of 7.05

Use 8 instead of 8.4


Solve $$\displaystyle\frac{0.4x+1}{7-0.05x}=8~:$$

Multiplying both sides by $$7-0.05x$$ eliminates the denominator on the left and gives

$$0.4x+1=56-0.4x ~~\rightarrow~ ~0.8x=55$$

You can Ballpark $$x$$ to be close to 70 since $$0.8\cdot70 = 56$$.

Now solve and POE answer choices that do not fall in the right ballpark. You can easily eliminate all negative answers and 145 is much too large, thus the correct answer is D.

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