Company A’s output of 245 widgets per week is 35 percent of Company B’s weekly widget output.
| Quantity A | Quantity B |
| 700 | Company B’s weekly widget output. |
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Solution
Translate the question into a percent formula. So, “245 widgets per week is 35 percent of Company B’s weekly widget output” means 245 = \(\frac{35}{10}\) × B.Try Plugging In Quantity A into this formula. Does \(\frac{35}{10}\) × 700 = 245? Yes, so the quantities must be equal.
Which of the following inequalities is true?
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Solution
Convert the fractions to decimals to see which inequality is correct.You can divide them out (remember, numerator divided by denominator), but it might help to have some common fraction/decimal equivalents memorized. Starting with choice (A),\(\frac{1}{11}\approx 0.09\), so this inequality is not true.Convert the fractions in choice (B): 0.1 < 0.11 < 0.125; this inequality is true.
| Quantity A | Quantity B |
| 7⁄8 – 0.25 | 0.325 + 1⁄3 |
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Solution
Convert the fractions to decimals. So 7⁄8=0.875, making Quantity A 0.625. In Quantity B,1⁄3 is about 0.333, making Quantity B about 0.658. Quantity B is greater.
The Warm Muffin Bakery’s cookie sales are always 60 percent of its muffin sales. What would be the increase in The Warm Muffin Bakery’s cookie sales if its muffin sales increased from 10,000 to 20,000?
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Solution
If The Warm Muffin Bakery sells 10,000 muffins, it sells 6,000 cookies. If the Warm Muffin Bakery then sold 20,000 muffins, it would sell 12,000 cookies.The cookie sales would thus increase by 6,000.
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Solution
You have far too many fractions to add quickly with the Bowtie. Instead, convert all of the fractions to the common denominator of \(48:\frac{1}{48}+\frac{1}{48}+\frac{1}{12}+\frac{1}{8}+\frac{1}{4}+\frac{1}{2}=\frac{1+1+4+6+12+24}{48}=\frac{48}{48}=1\)
If 20 percent of x is 5y, and y = 7, what is 60 percent of x?
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Solution
Begin by Plugging In 7 for y, so 20 percent of x is 35.You could go on to solve for x, but a shortcut would be to say that 60 percent of x is three times 20 percent of x, so multiply 35 by 3 to get 105.
Rohan began a savings account with a balance of $200. His current balance is $150.
| Quantity A | Quantity B |
| The percent decrease from Rohan’s original balance to his current balance | The percent increase that would returnRohan’s current balance to his original balance |
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Solution
The percent change formula is \(\frac{difference}{original}\times 100\).Remember that the “original” is the amount before the change. So, in Quantity A, the difference is 200 − 150 = 50, and the original is 200, which yields a 25% change. In Quantity B, the difference is also 50, but the number changes from 150 to 200, so the “original” is 150, which yields roughly a 33.3% change.Thus, Quantity B is greater
Joey works at a clothing store and receives an employee discount of 10 percent o3 the regular price of any item. What is the regular price of an item that Joey purchases for $99?
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Solution
With his employee discount, Joey purchases an item for 90% of its regular price, so 90% of the regular price of this item is equivalent to $99 or \(\frac{90}{100}x=99\). Solve for x to find that the regular price is $110.
| Quantity A | Quantity B |
| The change in price of a pair of shoes marked down by 50% | The change in price of a pair of boots marked down by 30% |
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Solution
Be careful:You’re not given the original price of either pair of shoes, and because you can’t assume they’re the same price, try Plugging In a variety of values. If the shoes in both quantities originally cost 10 dollars, then the change in price of the shoes in Quantity A is 5 dollars, and the change in price of the shoes in Quantity B is 3 dollars; Quantity A is greater, so eliminate choices (B) and (C). If the shoes in Quantity B originally cost 20 dollars, though, then the change in price is 6 dollars. Quantity B is now greater, so eliminate choice (A), and you’re left with choice (D), the correct answer.
A deposit at a local bank earns between 2 percent and 5 percent simple interest in a year. If Shirley makes an initial deposit of $800 at the bank, which of the following could be the amount of money in her account at the end of one year?
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Solution
5% of $800 is $40, thus, the maximum amount of money that could be in the account at the end of one year is $840; eliminate choices (C), (D), and (E). Similarly, the minimum amount that could be in the account at the end of one year is $800 plus 2% of $800, or $816; eliminate choice (A).