SSAT Upper Level Math : How to solve algebraic word problems

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #1 : Algebraic Word Problems

Michael scores a 95, 87, 85, 93, and a 94 on his first 5 math tests. If he wants a 90 average, what must he score on the final math test?

Possible Answers:

Correct answer:

Explanation:

To solve for the final score:

Add the five past test scores and you get 454. Then set up an algebraic equation where you add 454 to , which is the final test score, and divide by six, because you want the average for 6 tests now. You make this equation equal to 90 because that is the average Michael wants and solve for :

Example Question #2 : Algebraic Word Problems

If David wants to drive to his friend's house, which is 450 miles away, in 6 hours, what is the average speed David has to drive at?

Possible Answers:

Correct answer:

Explanation:

 

Plug in the the values for distance and time, and solve for rate.

 

and 

 

 

Example Question #1 : Algebraic Word Problems

If the sum of the smallest and largest of three consecutive even numbers is 28, what is the value of the second largest number in the series?

Possible Answers:

Correct answer:

Explanation:

The three numbers would be

, and .

Add the first and third value and you get

 

and

.

The second largest value is .

Example Question #4 : Algebraic Word Problems

Beth and Sam are 500 miles apart. If Beth travels at 60mph and leaves her house at 1pm, what time will she arrive at Sam's house? 

Possible Answers:

9:00 PM

9:33 PM

8:33 PM

9:30 PM

9:20 PM

Correct answer:

9:20 PM

Explanation:

Using , the time would be  hours, which is  hours and  minutes. If you add that to 1pm, you get 9:20pm.

Example Question #5 : Algebraic Word Problems

Greg is trying to fill a 16 oz. bottle with water. If Greg fills the bottle at 1 oz per second and the bottle leaks .2 oz per second, how long would it take for Greg to fill the bottle?

Possible Answers:

Correct answer:

Explanation:

You first find the rate at which the bottle is being filled at, which is  

.

Then you divide the entire bottle, which is  by the rate of , and you get

Example Question #6 : Algebraic Word Problems

Barbara went to the store and bought a shirt for  dollars. It had been discounted by 20%. What is the original price of the shirt?

Possible Answers:

Correct answer:

Explanation:

To get the final price, you use  as the variable for the original price. So,

, and divide by 0.8 on both sides of the equations, and you get

 for the original price of the shirt.

Example Question #7 : Algebraic Word Problems

Two inlet pipes lead into a large water tank. One pipe can fill the tank in 45 minutes; the other can fill it in 40 minutes. To the nearest tenth of a minute, how long would it take the two pipes together to fill the tank if both were opened at the same time?

Possible Answers:

Correct answer:

Explanation:

Look at the work rates as "tanks per minute", not "minutes per tank".

The two pipes can fill the tank up at  tanks per minute and   tanks per minute. 

Let  be the time it took, in minutes, to fill the tank up. Then, since rate multiplied by time is equal to work, then two pipes filled up  and  tanks; together, they filled up  tank - one tank. This sets up the equation to be solved:

 minutes

Example Question #8 : Algebraic Word Problems

The inlet pipe to a large water tank can fill the tank in 25 minutes; the drain of the tank can empty it in 55 minutes. 

Once, the drain was left open by mistake when the tank was being filled. The mistake was not caught until the tank was full. To the nearest tenth of a minute, how long did it take to fill the tank?

Possible Answers:

Correct answer:

Explanation:

Look at the work rates as "tanks per minute", not "minutes per tank".

The inlet pipe can fill the tank at a rate of  tank per minute. The drain is emptying the tank at a rate of  tank per minute.

Let  be the time it took, in minutes, to fill the tank up. Then, since rate multiplied by time is equal to work, then the inlet pipe let in  tank of water, but the drain let out  tank. Since they were working against each other, the work of the latter is subtracted from that of the former, and we can set up and solve the equation:

 minutes

Example Question #1 : Algebraic Word Problems

One angle of a pentagon measures . The other four angles are congruent to one another. Give the measure of one of those angles in terms of .

Possible Answers:

Correct answer:

Explanation:

The total of the measures of the angles of a pentagon is

.

One angle measures ; since the other four angles have the same measure as one another, we let  be their common measure. Then we set up the equation and solve for :

Example Question #10 : Algebraic Word Problems

John and Julie represented West High in a math contest. John outscored Julie by 16 points; as a team, they scored 80 points.

David and Dana represented East High in the same contest. Dana outscored David by 10 points; as a team, they scored 60 points.

Arrange the four students from highest score to lowest score.

Possible Answers:

Dana, John, David, Julie

John, Dana, Julie, David

John, Dana, David, Julie

John, Julie, Dana, David

Dana, John, Julie, David

Correct answer:

John, Dana, Julie, David

Explanation:

Let Julie's score be . Then John's score was . Since the sum of their scores was 80,

Julie scored 32, and John scored 16 higher, or 48.

 

Let David's score be . Then Dana's score was . Since the sum of their scores was 60,

David's score was 25, and Dana's score was 10 higher, or 35.

 

In descending order of score, the students were John, Dana, Julie, David.

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