Question

A group of 2 adults and 4 children spent $38 on tickets to a museum. A group of 3 adults and 3 children spent $40.50 on tickets to the museum. Based on this information, how much is an adult ticket, and how much is a child ticket?

2a + 4c = 38.00

3a + 3c = 40.50

What values of a and c represent the solution to the system?

a = c =

Answer 1

the answer is :38 -16 = 22

`22 / 4 = 5.5`

`40.50 - 24 = 16.50`

`16.50 / 3 = 5.50`
adults $8 childrens 5.5

Answer 2

Adult ticket = $8

Child ticket = $5.5

a = 8 and c = 5.5

Explanation:

2a + 4c = 38

3a + 3c = 40.5

To solve for the value of a and c in these equations. We solve the simulatenous equation by substitution method.

2a + 4c = 38 ..........eqn1

3a + 3c = 40.5 ............eqn2

Step 1, Find the value of a in eqn1

2a + 4c = 38

2a = 38 - 4c

a = (38-4c)/2

a = 19 - 2c

Step 2, subtitle the value of a in eqn2 to get the value of c.

3a + 3c = 40.5

3(19-2c) + 3c = 40.5

57 - 6c +3c = 40.5

57-40.5 = 6c -3c

16.5 = 3c

c = 16.5/3

c = 5.5

Step 3, subtitle the value of c in eqn1 to get the value of a.

2a + 4c = 38

2a + 4(5.5) = 38

2a + 22 = 38

2a = 38-22

2a = 16

a = 16/2

a = 8

Therefore:

Adult ticket = $8

Child ticket = $5.5

a = 8 and c = 5.5