A local electronics store sold 80 laptop computers in January. In February, the store’s laptop sales were of January’s sales. How many laptop computers did the store sell in February?

Solution available with step-by-step explanation

SAT Percentages Question 25 | Free SAT Prep | Aniko

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Question 25·Easy·Percentages

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A local electronics store sold 80 laptop computers in January. In February, the store’s laptop sales were $135\%$ of January’s sales. How many laptop computers did the store sell in February?

For percent problems that say something is a certain percent of a starting value, immediately translate the phrase into multiplication: “X% of N” becomes $(X/100) \times N$ . If the percent is more than 100, think of it as $100\%$ plus an extra amount (for example, $135\% = 100\% + 35\%$ ), which means the new amount is the original plus that extra percent of the original. This approach avoids setting up equations and lets you solve quickly by turning the percent into a decimal multiplier and doing a single multiplication.

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Translate the percentage phrase into math

Focus on the phrase “135% of January’s sales.” How do you usually represent “X% of” a number in math form?

Convert the percent to a decimal or fraction

Write 135% as a decimal or a fraction over 100. What number should you multiply 80 by?

Use the idea of 100% plus extra

Think of 135% as 100% of January’s sales plus an extra 35% of January’s sales. What is 35% of 80, and what do you do with that amount?

Desmos Guide

Use Desmos to compute 135% of 80

In a new expression line, type 80*1.35 (or 80*135/100). The value that Desmos displays is the number of laptop computers sold in February.

Step-by-step Explanation

Understand what 135% of January’s sales means

The phrase “February’s sales were 135% of January’s sales” means that the number of laptops sold in February is 135% of 80, the January amount. In math, “135% of 80” means you multiply 80 by 135% written as a number (decimal or fraction).

Convert 135% to a multiplier and set up the calculation

Percent means “per 100,” so

$135\% = \dfrac{135}{100} = 1.35$ .

So, February sales can be written as:

\text{February sales} = 80 \times 1.35

(Alternatively, you can think of this as $100\% + 35\%$ , or the original 80 plus 35% of 80.)

Compute the number of laptops sold in February

Now multiply:

80 \times 1.35 = 80 \times (1 + 0.35) = 80 + 0.35 \times 80

Find $35\%$ of 80:

$10\%$ of 80 is $8$ .
$30\%$ of 80 is $3 \times 8 = 24$ .
$5\%$ of 80 is half of $10\%$ , so $4$ .
So $35\%$ of 80 is $24 + 4 = 28$ .

Then add this to the original 80:

80 + 28 = 108

So, the store sold 108 laptop computers in February.

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Desmos Guide

Step-by-step Explanation

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Desmos Guide

Step-by-step Explanation