Algebra question please help

Question

The circus is in town.Admission for 3 adults and 4 children is $30 dollars while the admission for 2 adults and 5 children is $28.75. What is the price of each ticket? Adult tickets____ childrens tickets___

Answer 1

Hi, Esme!

 

Okay, so let:

X = price of adult ticket

Y = price of child's ticket

Then,

3X + 4Y = 30

2X + 5Y = 28.75

 

Now, we can multiply these equations:

2(3X + 4Y = 30) = 6X + 8Y = 60

3(2X + 5Y = 28.75) = 6X + 15Y = 86.25

 

Now we can solve:

 

 

 6X +15Y = 86.25

-6X - 8Y   =-60

_______________

7Y = 26.25

Y = 3.75

Then substitute into original equation:

3X + 4(3.75) = 30

3X = 15

X = 5

 

Therefore:

Adults = $5.00

Children = $3.75