# SYSTEMS OF LINEAR EQUATIONS â€“ WORD PROBLEMS

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```					                         SYSTEMS OF LINEAR EQUATIONS – WORD PROBLEMS

1. It takes Cathy 1.5 hours to paddle her canoe 6 miles upstream. Then she turns her canoe around and paddles
6 miles downstream in 1 hour. What is the rate of the current? What is Cathy’s paddling rate in still water?

2. With a tailwind, a jet flew 2000 miles in 4 hours. The jet’s return trip against the same wind required 5
hours. Find the jet’s speed and the wind speed.

3. With a tailwind, a helicopter flies 300 miles in 1.5 hours. When the helicopter flies back against the same
wind, the trip takes 3 hours. What is the helicopter’s speed? What is the wind’s speed?

4. Allyson paddles her canoe 9 miles upstream in 4.5 hours. The return trip downstream takes her 1.5 hours.
What is the rate at which Allyson paddles in still water? What is the rate of the current?

5. With a tailwind, a plane makes a 3000-mile trip in 5 hours. On the return trip, the plane flies against the
same wind and covers the 3000 miles in 6 hours. What is the speed of the wind?

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6. A chemist mixed a 15% glucose solution with a 35% glucose solution. This mixture produced 35 liters of a
19% solution. How many liters of each solution did the chemist use in the mixture?

7. A 4% salt solution is mixed with a 15% salt solution. How many milliliters of each solution are needed to
obtain 600 milliliters of a 10% salt solution?

8. A jar contains quarters and dimes. There are 15 more quarters than dimes. The total value of the coins is
\$23. How many of each coin are there?

9. Donnell wants to make a 2-pound mixture of cashews and pecans that costs \$2.60 per pound. Cashews cost
\$2.50 per pound and pecans costs \$3.00 per pound. How many pounds of each should he use?

10. At the Snack Shack, dried cherries cost \$3.50 per pound. Dried apricots cost \$1.50 per pound. The store’s
owner wants to make 10 pounds of a cherry-apricot mixture that costs \$2.70 per pound. How many pounds of
cherries and apricots should the owner use to make the mixture?

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11. The sum of the digits of a two-digit number is 14. When the digits are reversed, the new number is 36
more than the original number. What is the original number?

12. The sum of the digits of a two-digit number is 10. If 18 is added to the number, the digits will be reversed.
Find the number.

13. The sum of the digits of a two-digit number is 14. The first digit is 4 less than twice the second digit. What
is the number?

14. Alex is 6 years older than Frank. The sum of their ages is 50. Find Alex’s age and Frank’s age.

15. Leticia is 21 years older than Katie. In 2 years, Leticia will be twice as old as Katie. Find Leticia’s current
age and Katie’s current age.
NOTES: SYSTEM OF LINEAR EQUATIONS

I. SOLVING RATE PROBLEMS                                             2. With a tailwind, an airplane makes a 900-mile trip in 2.25 hours.
On the return trip, the plane flies against the wind and makes the trip
1. Ben paddles his kayak along a 9-mile course on a river. Going     in 3 hours. What is the plane’s speed? What is the wind speed?
upstream, it takes him 6 hours to complete the course. Going
downstream, it takes him 2 hours to complete the same course. What            Let ___ = __________________________________________
is the rate of the kayak? What is the rate of the current?
Let ___ = __________________________________________
Let ___ = __________________________________________

Let ___ = __________________________________________

Equations:

Solve:
Equations:

Solve:

II. SOLVING MIXTURE PROBLEMS                                           2. A coin bank contains 250 dimes and quarters worth a total of
\$39.25. Write and solve a system of linear equations to find how
1. A pharmacist wants to mix an ointment that is 9% ointment zinc      many dimes and quarters there are in the coin bank.
oxide with an ointment with an ointment that is 15% zinc ointment to
make 30 grams of an ointment that is 10% zinc oxide. How many                   Let ___ = __________________________________________
grams of each ointment should the pharmacist mix together?
Let ___ = __________________________________________
Let ___ = __________________________________________

Let ___ = _________________________________________

Equations:

Solve:
Equations:

Solve:

III. SOLVING NUMBER-DIGIT PROBLEMS                                      2. The sum of the digits of a two-digit number is 10. When the digits
are reversed, the new number is 54 more than the original number.
1. The sum of the digits of a two-digit number is 17. When the digits   What is the original number?
are reversed, the new number is 9 more than the original number.
What is the original number? Check your answer.                                  Let ___ = __________________________________________

Let ___ = __________________________________________                    Let ___ = __________________________________________

Let ___ = __________________________________________           Original number: _________________ New number: _____________

Original number: _________________ New number: _____________
Equations:
Equations:
Solve:
Solve: