9.5 – Systems Applications
Algebra I 300
Name:
Date:
Use the four steps shown below to solve the following problems, using any Systems of
Equations method that you choose.
1) Define the variables:
2) Set up the Equations:
3) Solve the System:
4) Check the answer:
1. Mary invested $9,000 in stocks and bonds. The stocks paid 5% in interest and the
bonds paid 8% in interest, giving an annual income of $525. How much did she invest in
stocks and bonds?
2. At an amusement park, you get 5 points for each bull’s eye you hit, but you lose 10
points for every miss. After 30 tries, Yolanda lost 90 points. How many bull’s eyes did
she have?
3. Lisa and Beverly had just $5 to spend for an after-school snack. They could have
bought two hamburgers and 1 carton of milk with no change back or 1 hamburger and 2
cartons of milk with 40 cents change back. How much does a carton of milk cost?
9.5 – Systems Applications
Algebra I 300
Name:
Date:
4. Since my uncle’s farmyard appeared to be overrun with chickens and docs, I asked
him how many of each he had. Being a puzzler as well as a farmer, my uncle replied that
his dogs and chickens had a total of 148 legs and 60 heads. How many dogs and how
many chickens does my uncle have?
5. If Tom gives Maria 30 cents, they will have equal amounts of money. But if Maria
then gives Tom 50 cents, he will have twice as much money as she does. How much
money does each have now?
6. Three pizzas and four sandwiches cost $34. Three pizzas and seven sandwiches cost
$41.50. How much does a pizza cost?
7. Ted’s bill for 6 cans of grape juice and 4 cans of orange juice was $13.20. When he
got home, he found that he should have bought 4 cans of grape juice and 6 cans of orange
juice. Although he mixed up the order, Ted did save 60 cents. How much does each can
cost?
9.5 – Systems Applications
Algebra I 300
Name:
Date:
8. Marcia has $84 less than three times as much as Sue. Together they have $132. How
much money does Marcia have?
9. Todd has 48 words to spell for a puzzle. As an incentive, his mother offers to pay him
10 cents for each word he spells correctly, if Todd will pay her 6 cents for each word he
spells incorrectly. If Todd makes $1.92, how many words did he spell correctly?
10. Six grapefruit cost as much as a dozen oranges. The cost of a dozen grapefruit and
two dozen oranges is $12. How much does one grapefruit cost?
9.5 – Systems Applications
Algebra I 300
Solve by the Graphing Method.
11.
x  4y  2
2 y  3x  6
Solve the by the Substitution Method.
x y 5
12.
3x  2 y  10
Solve by the Elimination Method.
x y 7
13.
3x  2 y  11
Name:
Date:
9.5 – Systems Applications
Algebra I 300
Name:
Date:
Old Material Review:
14. Tickets for the senior class play cost $6 for adults and $3 for students. A total of 846
tickets were sold. How many student tickets were sold?
15. A bicycle rode up a mountain at 12 km/h and then back down at 30 km/h. If the
round trip took 3.5 hours, how long did the ride up the mountain take?
Rate
 3x y  3xy 
 3x y 
2
16.
Time
2
2
2
3
D=rt

 

17. 2 xyz  4 x 2 yz 2  8x 3 yz 2  yz 