Systems of Equations Word Problems Answer Sheet
Work must be attached for full credit (on loose-leaf paper)
Name: _____________________________________________
Date: ______________________________________________
Period: ____________________________________________
1. You will need to mix _______________ pounds of coffee worth $1.50/lb. with _____________ pounds of
coffee worth $2.00/lb. to obtain 3 lbs. of coffee that is worth $1.70/lb.
2. ____________ liters of 70% solution
3. You will need to mix ______________ pounds of raspberry-flavored gumdrops with _________________
pounds of cherry flavored jellybeans to obtain 20 pounds candy that can be sold for $1.10 per
pound.
4. ______________ liters of 20% solution
5. You will need to mix ________________ liters of 10% acid solution with ________________ liters of 30%
acid solution to obtain 10 liters of 15% acid solution.
6. You will need to mix approximately _____________________ gallons of 84 octane gasoline with
____________________ gallons of 91 octane gasoline to obtain 15,000 gallons of 89.7 octane gasoline.
7. a. ______________ outs made by infielders b. ___________ outs made by outfielders
8. a. ____________ hours doing yard clean up b. __________ hours painting
9. ____________ nickels and ___________ quarters
10. ___________ field goals and ___________ extra points
11. _____________ gallons of 50% acid solution and _______________ gallons of 25% acid solution
12. __________ ft by __________ ft
13. a. __________ years b. __________ inches
14. Scuba diver: ___________________ miles per minute, current: __________ miles per minute
15. There are ___________ kangaroo’s and __________ Llama’s
16. The row team paddles _____________ mph in still water and the current is __________ mph
MAFS.912.A-CED.1.2
MAFS.912.A-REI.3.6
Solve real-world problems involving systems of linear equations and inequalities in two and three
variables.
1. How many pounds of coffee worth $1.50 per pound should be mixed with coffee worth $2.00 per
pound to obtain 3 pounds of a new blend worth $1.70 per pound?
Amount
Unit Price
Value
Coffee worth
$1.50/pound
Coffee worth
$2.00/pound
Resulting Mixture
2. A Chemist wants to mix a 70% saline solution with a 8 liters of a 25% saline solution to create a
solution with 40% salt. How many liters of the 70% solution does she need?
Liters
Percentage
Value
70% solution
25% solution
Resulting 40 % solution
Equation 1 (# of liters): ________________________________
Equation 2 (Percentages): _______________________________________
3. Suppose the owner of a candy store mixes two types of candies. She decides to create a 20-pound
mixture of raspberry-flavored gumdrops and cherry-flavored jellybeans. The gumdrops sell for $0.95 per
pound and the jellybeans sell for $1.20 per pound. She plans to sell the mix for $1.10 per pound. How
many pounds of each candy should she use in her mix?
4. How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to
make a 30% solution?
5. Suppose you work in a lab…
You need a 15% acid solution for a certain test, but your supplier only ships a 10% solution and a 30%
solution. Rather than pay the hefty surcharge to have the supplier make a 15% solution, you decide to
mix 10% solution with 30% solution, to make your own 15% solution. You need 10 liters of the 15% acid
solution. How many liters of 10% solution and 30% solution should you use?
Amount
Percent
Value
10% Acid Solution
30% Acid Solution
Resulting Mixture
6. The Octane number of gasoline can be thought of as the percent of the compound octane in the
gasoline. For example, 89-octane gas would be 89% octane and 11% something else. Suppose
that a wholesaler has 84-octane gas and 91-octane gas, how much of each kind should be mixed to
fill an order for 15,000 gallons of 89.7-octane gas? (Round your answers to the nearest tenth)
7.
In a game, 12 out of a baseball team’s 27 outs were fly balls. Twenty-five percent of the outs made
my infielders and 100% of the outs made by outfielders were fly balls.
a. How many outs were made by infielders?
b. How many outs were made by outfielders?
8.
During the spring and summer, you do a spring yard cleanup for households and you also paint
houses. You earn $8 an hour doing the cleanups and $12 an hour painting. Last Spring and
summer, you worked a total of 400 hours and earned $3800.
a. How many hours did you spend doing the yard cleanups?
b. How many hours did you spend painting?
9. You have $4.30 in your piggy bank with only nickels and quarters. You have 8 more nickels than
quarters. How much of each coin do you have?
10. A field goal is 3 points and the field goal after a touchdown is only 1 point. In a recent post-season,
Adam Vinatieri of the Indianapolis Colts made a total of 21 field goals and extra point kicks for 49
points. Find the number of field goals and extra points he made.
11. Orion Labs needs to make 500 gallons of 34% acid solution. The only solutions available are a
25% acid solution and a 50% acid solution. Write and solve a system of equations to find the
number of gallons of each solution that should be mixed to make the 34% solution.
12. Corey has 42 feet of fencing around his garden. The garden is rectangular in shape and its length
is equal to twice the width minus 3 feet. Write a system of equations to find the length and width
of the garden. What is the length and width of the garden?
13. You plant a 14-inch hemlock tree in your backyard that grows at a rate of 4 inches per year and an
8-inch blue spruce that grows at a rate of 6 inches per year.
a. In how many years after you plant the trees will the two trees be the same height?
b. How tall will each tree be?
14. Scuba diver swims 0.08 miles upstream in 40 minutes. She then swims back downstream 0.1
miles in 10 minutes and passes the boat. How fast could the scuba diver swim without a current?
How fast is the current?
15. A small petting zoo has Llama’s and Kangaroo’s. There are 120 legs and 47 heads on this farm.
How many Llama’s and how many Kangaroo’s does the farm have?
16. A row team paddles 30 miles upstream in 2 hours and 30 miles downstream in 45 minutes. How
fast can the row team paddle in still water? What is the rate of the current?