Question

At a local museum, the total price for one adult and one child is $11. Mrs. Smith paid for herself and her three children. She spent $19. Record the system of equations to be solved and then find the price of an adult and child ticket using either elimination or substitution.

Answer 1

a+c =11

a +3c = 19

a =7 and c = 4

Explanation:

Let a = price of one adult

c = price of one child

We know one adult and one child = 11

a+c =11

Mrs smith and 3 children spent 19

a +3c = 19

We have 2 equations and 2 unknowns

a+c =11

a +3c = 19

Multiply the first equation by -1 so we can eliminate a

-a-c=-11

a+3c=19

----------------

2c = 8

Divide by 2

2c/2 = 8/2

c=4

Each child equals 4 dollars

Now we need to find a

a + c= 11

a+4 = 11

Subtract 4 from each side

a+4-4 = 11-4

a = 7

The adult is 7