Which system of equations below will determine the number of adult tickets, a,
and the .... KEY: Linear system | elimination | word problem. MSC: Application.
Name: ______________________
Class: _________________
Date: _________
ID: A
Solving Real-World problems with System of Linear Equations ____
1
Mr. Frankel bought 7 tickets to a puppet show and spent $43. He bought a combination of child tickets for $4 each and adult tickets for $9 each. Which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought? A. a = c - 9 9a + 4c = 43 B. 9a + 4c = 43 a +c=7 C. a + c = 301 a +c=7 D. 4a + 4c = 50 a +c=7
____
2
Tyrone is packaging a mix of bluegrass seed and drought-resistant seed for people buying grass seed for their lawns. The bluegrass seed costs him $2 per pound while the drought-resistant grass seed costs him $3 per pound. a. Write an equation showing that Tyrone spent $68 altogether for the two types of grass seed. b. Write an equation showing that Tyrone bought a total of 25 lb of the two types of grass seed. c. Solve the system of equations to find out how many pounds of each type of grass seed Tyrone bought.
3
Mr. Jarvis invested a total of $9,112 in two savings accounts. One account earns 7.5% simple interest per year and the other earns 8.5% simple interest per year. Last year, the two investments earned a total of $884.88 in interest. Write a system of equations that could be used to determine the amount Mr. Jarvis initially invested in each account. Let x represent the amount invested at 7.5% and let y represent the amount invested at 8.5%. A.
x + y = 9, 112
C.
0.075x + 0.085y = 884.88 B.
x + y = 884.88 0.075x + 0.085y = 9, 112
x + y = 884.88
D.
7.5x + 8.5y = 9, 112
x + y = 9, 112 7.5x + 8.5y = 884.88
4
A rental car agency charges $15 per day plus 11 cents per mile to rent a certain car. Another agency charges $18 per day plus 8 cents per mile to rent the same car. How many miles will have to be driven for the cost of a car from the first agency to equal the cost of a car from the second agency? Express the problems as a system of linear equations and solve using the method of your choice.
5
The table below shows the costs of two different combinations of hot dogs and sodas at a ballgame. What is the cost h of one hot dog and the cost s of one soda? Number of hot dogs 4 4
Number of sodas 4 6
1
Total Cost $20 $24
Name: ______________________
____
ID: A
6
Find two numbers whose sum is 33 and whose difference is 13.
7
A boat travels with the current at a speed of 10 miles per hour with respect to land, then against the same current at a speed of 6 miles per hour with respect to land. Find (a) the speed of the current, and (b) the speed of the boat in still water.
8
Marc sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Marc's sales totaled $1624. How many adult tickets and how many student tickets did Marc sell? F. 220 adult, 241 student G. 225 adult, 236 student
9
H. 236 adult, 225 student I. 241 adult, 220 student
x pounds of candy valued at $3.50 per pound is mixed with y pounds of candy valued at $4.30 per pound to produce 10 pounds of a mixture selling for $4 per pound. Find x and y, the number of pounds of each type.
2
ID: A
Solving Real-World problems with System of Linear Equations Answer Section 1
2
3
4
5
6
ANS: B PTS: 1 DIF: 1 TOP: Lesson 7.1 Solve Linear Systems by Graphing KEY: word | system | equations | simultaneous NOT: 978-0-547-22197-7 ANS: a. 3x + 2y = 68 b. x + y = 25 c. drought-resistant: 18 lb; bluegrass: 7 lb
MSC: Knowledge
PTS: 1 DIF: 2 STA: MA.912.A.3.11 | MA.912.A.3.14 TOP: Lesson 7.1 Solve Linear Systems by Graphing KEY: application | system | linear MSC: Application NOT: 978-0-547-22197-7 ANS: A PTS: 1 DIF: 1 TOP: Lesson 7.2 Solve Linear Systems by Substitution KEY: solve | word | system MSC: Comprehension NOT: 978-0-547-22197-7 ANS: c = 15 + 0.11m c = 18 + 0.08m 100 miles PTS: 1 DIF: 2 STA: MA.912.A.3.13 | MA.912.A.3.14 TOP: Lesson 7.2 Solve Linear Systems by Substitution KEY: solve | equation | word | system | linear MSC: Application NOT: 978-0-547-22197-7 ANS: h = $3.00, s = $2.00 PTS: 1 DIF: 2 TOP: Lesson 7.3 Solve Linear Systems by Adding or Subtracting KEY: Linear system | elimination | word problem MSC: Application NOT: 978-0-547-22197-7 ANS: 23 and 10 PTS: TOP: KEY: NOT:
1 DIF: 3 Lesson 7.3 Solve Linear Systems by Adding or Subtracting Linear system | elimination | word problem MSC: Comprehension 978-0-547-22197-7
1
ID: A 7
8
9
ANS: a. 2 miles per hour b. 8 miles per hour PTS: 1 DIF: 2 TOP: Lesson 7.3 Solve Linear Systems by Adding or Subtracting KEY: Linear system | elimination | word problem MSC: Application NOT: 978-0-547-22197-7 ANS: I PTS: 1 DIF: 2 STA: MA.912.A.3.13 | MA.912.A.3.14 TOP: Lesson 7.4 Solve Linear Systems by Multiplying First KEY: linear | variables | two | equation | word | system MSC: Application NOT: 978-0-547-22197-7 ANS: x = 3.75 lb; y = 6.25 lb PTS: TOP: KEY: NOT:
1 DIF: 2 STA: MA.912.A.3.13 | MA.912.A.3.14 Lesson 7.4 Solve Linear Systems by Multiplying First solve | word | system | linear | write MSC: Application 978-0-547-22197-7
2
