Word Problems with Percents, Ratios, and Rates

Most of the percentage problems on the test actually come in word form. Since we already know how percentages work, we will delve right into these word problems starting with a few examples.

Chris earns a commission of 17 percent of the selling price of each television and 23 of the selling price of each DVD player that he sells. In one day, he sold four televisions each worth $988, and two DVD players each worth $127. How much did he earn in commission on that day?

4 × (988 × .17) + 2 × (127 × .23)

= 4 × 167.96 + 2 × 29.21

= 730.26

Chris made $730.26

Shoji and Anna sell jeans on their Web site. One pair costs $29.99. If you buy ten pairs, then you get 10% off. If you buy 100 pairs, then you get 30% off. How much do Shoji and Anna make if they sell 10 pairs to one customer and 100 pairs to another customer?

Difference = ((29.99 × 10) x .10) + ((29.99 × 100) × .3))

We have to remember to use the Order of Operations here, which states that multiplication must be done before addition. The full order is PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction).

Difference = (299.90 × .10) + (2999 × .3)

Difference = 29.99 + 899.7 = 929.69

Profit = (299.90 + 2999) – 929.69

Profit = 3298.9 – 929.69 = 2369.21

Other common word problems use ratios and rates. We have already reviewed ratios and rates, so let’s move on to some examples expressed as a word problem.

There are five oranges in a bag, along with three apples and two plums. What is the ratio of apples to oranges and plums to apples?

Oranges = 5

Apples = 3

Plums = 2

Apples to Oranges: 3:5

Plums to Apples: 2:3

Taking the above into consideration, what is the ratio of oranges to total fruit?

Total fruit = 5 + 3 + 2 = 10

Oranges to Total Fruit: 5:10 = 1:2

Rates. If Jim jogs 12 miles in five hours, what is his average speed?

Speed = 12 / 5

Speed = 2.4 miles per hour

Using the data from the above question, if Jim continues jogging at the same rate without stopping for another three and a half hours, how much distance will he cover?

Distance = rate × time

Distance = 2.4 × 3.5

Distance = 8.4 miles

That is about all there is for ratios, percentages, and rates in word problems. Having covered these topics in arithmetic form makes things much easier when you begin to tackle the word problems.

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