Question

A social worker earns an average bi-weekly net pay of $1,465.87. Which compound inequality correctly shows the amount of money, m, the social worker can spend if the monthly budget for food is between 10% and 20%?

$317.61 ≤ m ≤ $635.21
$293.17 ≤ m ≤ $586.35
$146.59 ≤ m ≤ $293.17
$476.41 ≤ m ≤ $635.21

Answer 1

(c) $146.59 ≤ m ≤ $293.17

Explanation:

You want the range of values that represents 10% to 20% of $1,465.87.

Ten percent

Ten percent is 10% = 10/100 = 1/10. This fraction of a decimal number is easily calculated by moving the decimal point to the left one place (dividing the number by 10).

10% · $1465.87 = $146.587

This rounds to $146.59.

At this point, you know enough to choose the correct answer to the question. The only answer choice with a lower limit of $146.59 is ...

$146.59 ≤ m ≤ $293.17

Twenty percent

Of course 20 is 2 times 10, so 20% = 2×10%, and ...

20% · 1465.87 = 2(10% · 1465.87)

= 2(146.587) = 293.174 ≈ 293.17

This confirms the upper end of the range of the budget for food.

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Additional comment

You may have noticed that the upper limit is not double the lower limit. (2×146.59 = 293.18 ≠ 293.17) This is because we don't want to use rounded values in the calculation. Rather, we want to save rounding until the last step after all calculations are made.