Use Equations to Solve Problems

14 school festival tickets were sold to adult and children. A total of $38 was collected from these ticket sales. Adult tickets cost $4 each and child tickets cost $1 each. The system of linear equations below represents, x, the number of adult tickets sold, and y, the number of child tickets sold.

x + y = 14

4x + y = 38

How many tickets were sold?

• 6 adult tickets and 8 child tickets

• 8 adult tickets and 6 child tickets

• 10 adult tickets and 4 child tickets

• 12 adult tickets and 2 child tickets

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

Kaya and Tad started with the same number of baseball cards in their collections. Kaya collected 3 cards per week and now has 29 cards. Tad collected 2 cards per week and now has 20 cards. Let x represent the number of cards they began with, and let y represent the number of weeks. Which system of equations represents this situation?

• x + y = 20

  3x + 2y = 29

• 5y = 49

  x + 20 = 29

• x + 3y = 20

  x + 2y = 29

• x + 3y = 29

  x + 2y = 20

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

The perimeter of a triangle is 16 inches. The length of its base is 2 times the length of one of its other two sides, which are equal. In the equation below, x represents the length of each of its equal sides, and y represents the length of its base.

2x + y = 16

y = 2x

What are the side lengths of the triangle?

• 3 in, 3 in, 6 in

• 4 in, 4 in, 8 in

• 4 in, 8 in, 8 in

• 6 in, 6 in, 8 in

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.SSE.A.1

Heidi paid $18 for 7 pairs of socks. She bought wool socks that cost $3 per pair and cotton socks that cost $2 per pair. Let x represent the number of wool socks and y represent the number of cotton socks. Which system of equations represents this situation?

• x + y = 7

  2x + 3y = 18

• x + y = 7

  3x + 2y = 18

• x + y = 18

  3x + 2y = 7

• x + y = 18

  x + y = 7

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

A jar contains only dimes and nickels. The total number of coins in the jar is 15. The total value of the coins is $1.00. How many of each type of coin are in the jar?

• 5 dimes and 10 nickels

• 7 dimes and 8 nickels

• 8 dimes and 7 nickels

• 10 dimes and 5 nickels

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

Two numbers have a sum of 139 and a difference of 31. Which is one of the numbers?

• 85

• 100

• 91

• 108

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.REI.C.6