ALGEBRA
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Name: __________________________ Date: _____________
1. For 5x 2y = 4, find y given x = 2.
2.
For
1 1 1
x y z + = ?
, find x given y = 2 and z = 5. Show your work.
3. How many liters of a 10% acid solution must be mixed with 5 liters of a 25% acid
solution to give a 15% solution?
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4. Find the x- and y-intercepts of x + 3y + 2 = 0 and use these intercepts to graph the
equation.
5. Find the slope of the line that contains the points (8, 6) and (7, 2). Show your work.
6. The price of a 2-hour plumbing repair job is $140 and the price of a 5-hour job is $290.
Use the slope to predict the cost of a repair job lasting 3 hours. Show your work.
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7. The Partrick County 4-H club has $500 to spend on trees for the club’s orchard. The
club votes to plant both apple trees and pear trees. If pear trees cost $40 each and apple
trees cost $25 each, write an equation in standard form that models the situation. Use x
for the number of apple trees and y for the number of pear trees and ignore sales tax.
8. If a ball is dropped from the top of a 360-foot building, then the formula h(t) = 360
16t2 expresses its height h(t) in feet as a function of the time t in seconds. Find h(3), the
height of the ball 3 seconds after it is dropped.
9. Solve the system of linear equations by the substitution method.
5
3
1 5 2
5
y x
x y
= ?
+ =
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10. Solve the system of linear equations.
1 1 1
2 3 3
1 1 2
6 3 9
x y
x y
+ =
+ =
11. Charles invested $18,900 in two mutual fund accounts: the Abernathy Fund and the
Brice Fund. During the subsequent year, The Abernathy Fund earned 8% and the Brice
account earned 4%. At the end of the year, the total interest earned was $1,064. How
much did Charles invest in each fund? Show your work.
12. Audrey has 32 dimes and quarters in her piggy bank with a total value of $6.50. How
many of the coins are dimes and how many are quarters?
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13. Vanessa recently received a $75,000 inheritance. She invested the money in three
accounts bearing 6%, 8%, and 12% simple interest. The amount invested at 8% was
three times that invested at 12%. If her total interest after one year was $5,700, how
much did she invest in each account?
14. Simplify.
( ) ( )
4 2 1 4m 3 4
3 3 m? ?
15. Faye invests $13,000 in a mutual fund that earns 5% compounded annually. How much
will the investment be worth in five years?
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16. The average salary for major league baseball players over the past two decades can be
modeled using the formula S(x) = 0.00436×2 0.00465x + 0.188, where S(x) is the
average salary in millions of dollars and x is the number of years since the 1980 season.
Use the formula to predict the average salary in the year 2007. Round to two decimal
places.
17. A well pump on a ranch can fill a 400 gallon watering trough in 90x minutes. What is
the pumping rate in gallons per minute?
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18. Hugo empties his piggy bank onto his kitchen table. After the coins come to rest,
one-fourth of the nickels are heads up, two-thirds of the dimes are heads up, and
one-half of the quarters are heads up. The figure below shows the composition of the
coins that were in the piggy bank. Use the figure and the given information to determine
the percentage of coins that are heads up.
Nickels, 1/6
Dimes, 1/3
Quarters, 1/2
19. Steve can weed his garden in 90 minutes. Steve’s daughter Amanda weeds one and
one-half times faster than Steve. How long would it take them to weed Steve’s garden
together? Show your work.
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20. A church group planned a cruise retreat that had a fixed cost of $30,000. Later, 20
more people decided to go, causing the average cost to decrease by $50 per person.
How many persons were planning to go on the retreat originally? Show your work.
