The Math Lesson - Level 3

Algebra Word Problems For grades 7 to 11

Each section has verbal problems which you should do with your child first.
Over 100 to 250 problems of graduated difficulty, with examples in each section.

Examples:

Problem 1: If 21 cows can be kept on 7 acres for 5 months, how many sheep can be kept on 10 acres for 6 months, if 8 sheep eat as much as 1 cow?

Answer: 21 divided by 7 tells us that 3 cows can be kept on 1 acre for 5 months. 15 cows can be kept on 1 acre for 1 month. 150 cows can be kept on 10 acres for 1 month. 35 cows can be kept on 10 acres for 6 months. 35 times 8 sheep can be kept or 280 sheep.

Problem 2: Reena is 25 years old, and 4 fifths of her age is 4 years less than twice Mina’s age; what is Mina’s age?

Answer: 4 fifths of 25 years is 20 years, which is 4 years less than twice Mina’s age; hence twice Mina’s age is 20 + 4, or 24 years, and her age is one half of 24, or 12 years.

And more:

Two cars leave leave a town at speeds of 60 and 80 mph. If they left a 3 pm, at what time, will the slower car have traveled 40% less distance than the fast car?

If she had biked home 2 miles per hour faster, she would have got home in 25% less time. But if she had biked 2 miles per hour slower, then she would have to spend one hour more on the way. How far is her home?

These problems first show up in Algebra word problems and then on SAT tests. If you follow our step by step program, your child will be able to do all of these problems quickly in his/her head.

Work and rate problems
Example: A works 4 times as fast B. Together they can do all the work in 4 days. How many days would each require alone?
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Age relationships
Example: The ages of two persons are respectively 42 years and 21 years. In how many years will the older person be twice as old the younger?
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Number relationships
Example: A number is three less than four times another number. Their sum is one
hundred two. What are the numbers?
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Speed and distance
Example: Two cars travel 72 miles over the same route. One travels 2 miles per hour faster than the other and makes the run in 30 minutes less time. Find the rate of each.
This is demo of the type of problems included in the full version.
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