Question

Lily is selling ice cream cones and ice cream sandwiches. She sells 3 ice cream cones and 4 ice cream sandwiches for $14.25. She sells 5 ice cream cones and 2 ice cream sandwiches for $13.25. How much is an ice cream cone? How much is an ice cream sandwich?

Answer 1

cost of ice cream cones = $1.75

cost of ice cream sandwiches = $2.25

Explanation:

Let

x = cost of ice cream cones

y = cost of ice cream sandwiches

3x + 4y = 14.25 (1)

5x + 2y = 13.25 (2)

Multiply (2) by 2

10x + 4y = 26.50 (3)

3x + 4y = 14.25 (1)

Subtract (1) from (3)

10x - 3x = 26.50 - 14.25

7x = 12.25

x = 12.25/7

x = $1.75

Substitute x = 1.75 into (1)

3x + 4y = 14.25

3(1.75) + 4y = 14.25

5.25 + 4y = 14.25

4y = 14.25 - 5.25

4y = 9

y = 9/4

y = $2.25

Answer 2

cost of ice cream cones = $1.75

cost of ice cream sandwiches = $2.25

Explanation:

Let

x = cost of ice cream cones

y = cost of ice cream sandwiches

3x + 4y = 14.25 (1)

5x + 2y = 13.25 (2)

Multiply (2) by 2

10x + 4y = 26.50 (3)

3x + 4y = 14.25 (1)

Subtract (1) from (3)

10x - 3x = 26.50 - 14.25

7x = 12.25

x = 12.25/7

x = $1.75

Substitute x = 1.75 into (1)

3x + 4y = 14.25

3(1.75) + 4y = 14.25

5.25 + 4y = 14.25

4y = 14.25 - 5.25

4y = 9

y = 9/4

y = $2.25