Algebra Word Problems Packet #1

On a separate sheet of paper, write your “Let” statement(s) to define the unknown.
Solve each problem using an algebraic equation.

1. Twice a number is 500 more than six times the number. What is the number?

2. Three-sevenths of a number is 24. Find the number.

3. What number increased by ¼ of itself is equal to 30?

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4. Find a number such that ¼ of the number is 50 less than of the number.
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5. The denominator of a fraction exceeds the numerator of a fraction by 25. The value of the
fraction is 3 . Find the fraction.
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6. If 6 times a number is decreased by 6, the result is the same as when 3 times the number
is increased by 12. Find the number.
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7. If 3 times a number is increased by 22, the result is 14 less than 7 times the number. What
is the number?

8. Separate 84 into two parts such that one part will be 12 less than twice the other.

9. The difference between two numbers is 24. Find the numbers if their sum is 88.

10. One number is 3 times another number. If 17 is added to each, the first resulting number is
twice the second resulting number. Find the two numbers.

11. The larger of two numbers is 1 less than 3 times the smaller. If 3 times the larger is 5 more
than 8 times the smaller, find the numbers.

12. The second of three numbers is one less than the first. The third number is 5 less than
twice the second. If the third number exceeds the first number by 12, find the three
numbers.

13. One number is 4 more than 5 times another number. If 6 is added to each, the first
resulting number is three times the second resulting number. Find the two numbers.

14. When you started your homework assignment, your friend already had 6 exercises done.
You can do about 3 exercises per minute, whereas your friend can only do 2 exercises per
minute. How many minutes will it take you to catch up to your friend.
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15. It took Thomas 25 minutes longer to do his math homework than to do his French
homework. He spent a total of 2.25 hours on both subjects. How much time did he spend
on math?

16. Jesse earns $6 an hour babysitting for his younger brother. His mom gave him $71 last
week. This included his babysitting money and his $20 allowance. How many hours did
Jesse babysit?

17. Carol and Cathy are each saving money for a vacation. Carol started with $25 and saves
$7.50 a week. Cathy started with $10 and saves $10 a week. When will they have saved
the same amount?

18. One weekend Bill earned 3 times as much as Jim. Tom earned $5 more than Jim. In all,
they earned $60. How much did each earn?

19. The Maxwell children have hired a caterer to provide food for an anniversary party for their
parents. The caterer has quoted a price of $96 per person and is asking for an advance
payment of one-fourth of the total bill. If the advance payment is $1200, how many guests
are invited to the party?

20. Three children each contributed toward a birthday present for their mother. The oldest
contributed three times as much as the youngest, while the second oldest contributed 50
cents more than the youngest. If the present costs $10.50, how much did each contribute?

21. At a school game, student tickets were 50 cents each and adult tickets were $1 each. If
the total receipts from 900 tickets were $500, how many tickets of each kind were sold?

22. A salesman sold 200 pairs of slippers. Some were sold at $6 per pair and the remainder
were sold at $11 per pair. Total receipts from this sale were $1600. How many pairs of
slippers were sold at $6 each?

23. At a recent job fair, there were 2 as many inquiries about jobs in health care as in
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electronics and 50 less inquiries about teaching as electronics. A reported 430 inquiries
were made about all three fields. How many inquiries were made about teaching?

24. TriCity Taxi Company€charges $3 for the first mile and $0.20 for every tenth of a mile
thereafter. If your trip is measured in tenths of a mile, how far can you ride in a TriCity Taxi
for $12.

25. Adam can rent an apartment in the city and walk to work for $615 per month. He can rent
an apartment in the suburbs for $500 per month and take the train to work for $5 per day.
How many days will he have to work per month to make either choice equal financially?

26. A company needs a faster computer to enhance its e-business capabilities. The computer
can be purchased for $1890 or rented for $900 plus $90 per month. What is the maximum
number of months the computer could be kept so that it is cheaper to rent than to buy?