How to solve arithmetic word problems

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SSAT Upper Level Quantitative › How to solve arithmetic word problems

Questions 1 - 10
1

There are 500 students at the high school. There are only two menu options: chicken or fish. If 15% of students ordered fish, how many students ordered chicken?

Explanation

If 15% of students ordered fish, then 85% of the students must have ordered chicken. Then multiply 85% or .

2

What is the ratio of 3 gallons to 5 quarts?

\dpi{100} 12:5

\dpi{100} 3:5

\dpi{100} 5:3

\dpi{100} 3:1

Explanation

First convert gallons to quarts. There are 4 quarts in a gallon. So 3 gallons is equivalent to \dpi{100} 4\times 3=12 quarts.

Now we have 12 quarts to 5 quarts. This ratio cannot reduce, so our answer is 12:5.

3

Convert 15.68 to a percent.

1568%

15.68%

1.568%

156.8%

15680%

Explanation

To convert a number to a percent, you just multiply it by . So %.

4

Candidate A gets of the votes in an election.

Candidate B gets 35% of the votes.

If 2.8 million people votes, how many more votes than Candidate A did Candidate B receive?

Explanation

First we need to get and 35% in the same terms so that we can subtract one from the other. Since 7ths are repeating decimals, it will be easiest to use fractions.

.

Now we multiply this fraction by 2.8 million, which reduces nicely to , which equals 180,000.

5

What number can 1536 be divided by that would give no remainder?

Explanation

6

Bob gets paid an hour for the regular hours he works and an hour for any overtime hours he works. All hours over 40 in a week are considered overtime. If Bob works 44 hours this week, how much did he make?

Explanation

You first calculate how much he makes for normal hours, which is the number of hours works multiplied by the wage. So for normal hours, . For overtime, it is . Add the amount made in overtime and the normal hours and you get .

7

of a class of 36 students are boys. If 2 girls and 4 boys were to drop the class, what percentage of the class would be girls?

60%

55%

65%

70%

75%

Explanation

First determine how many boys and girls are currently in the class.

boys in the class, which means that there are 20 girls.

When the 6 students drop the new class size will be 30, which will be made up of girls and boys.

8

The menu of a local coffeehouse reads as follows:

Sandy orders some drinks for herself and some friends. She orders three cappuccinos, two iced teas, two cafe lattes, and an espresso. The sales tax is five percent. How much change does she receive back for a twenty-dollar bill?

A twenty-dollar bill isn't enough to buy the drinks.

Explanation

The three cappuccinos cost:

The two iced teas cost

The two cafe lattes cost

The espresso costs .

Add these amounts to get the cost before tax:

The tax is five percent of or:

Add both values in order to obtain the total cost after tax.

As a result, the change from a twenty-dollar bill is as follows:

9

Joe drove an average of 45 miles per hour along a 60-mile stretch of highway, then an average of 60 miles per hour along a 30-mile stretch of highway. What was his average speed, to the nearest mile per hour?

Explanation

At 45 mph, Joe drove 60 miles in hours.

At 60 mph, he drove 30 miles in hours.

He made the 90-mile trip in hours, so divide 90 by to get the average speed in mph:

10

What is the ratio of \dpi{100} 6\ inches to \dpi{100} 12\ feet

\dpi{100} 1:24

\dpi{100} 1:2

\dpi{100} 1:12

\dpi{100} 1:6

Explanation

First, we need to convert 6 inches into feet.

There are 12 inches in a foot. \dpi{100} \frac{6\ inches}{12\ inches}=\frac{1}{2}.

So 6 inches is equal to \dpi{100} \frac{1}{2} feet. Now our ratio is \dpi{100} \frac{1}{2} to \dpi{100} 12. To find this ratio we divide 12 by \dpi{100} \frac{1}{2}.

\dpi{100} 12\div \frac{1}{2}=12\times \frac{2}{1}=12\times 2=24.

So the ratio is 1:24.

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