This section assumes that the student knows how to solve basic first degree equations. In the problem section, the starred problems assume that the student also knows how to solve quadratic equations.

Just because you've put together an equation based on a word problem doesn't mean that you're finished. You have to solve the equation. And then, once you've found the unknown, you need to make sure you know what the question is, because if you don't answer the question that was asked, you won't have a correct solution!

And watch out - sometimes problem writers will ask you sneaky things just to trick you!

Sample #1

If Fred's age now is three times what it was 12 years ago, how old was Fred 12 years ago?

Solution #1

If F is Fred's age now, the equation is: F = 3(F - 12)

The solution to this equation is F = 18. However, the problem didn't ask what Fred's age is NOW; it asks what it was 12 years ago. So the answer is 18 - 12, or 6.

Sample #2

The sum of a number and 20 is three times the number. What is biggest prime number less than the number?

Solution #2

The equation is: N + 20 = 3N

The solution of the equation is: N = 10

The largest prime number less than 10 is 7.

 

1.

The sum of a number and 15 is one more than three times the number. What is the number?

2.

The product of a number and six is 30 more than the number. What is half of the number?

3.

Hera's age now is half of what it will be in 10 years. How old will Hera be 10 years?

4.

The population of a city was 142,000, and it increased at a rate of 1,200 every year until the population was 184,000. How many years did the population increase?

5.

The product of 5 and four more than a number is nine times the number. What is the number?

6.

The price of a book increased by 10%, and the new price is $13.20. What would the price of two books have been before the price change?

7.

Twice the sum of a number and five yields three times the sum of the number and 2. What is the number?

8.

* The product of a number and two more than the number is 48. What is the number?

9.

* The product of one less than a number and one more than a number is one less than ten times the number. What is the number?

10.

If a number is increased by four and the result is doubled, and this result is squared, this yields a number which is eight more than 68 times the original number. In what month does Christmas occur?