Question

It costs $35 for one adult and two children to attend a show It costs $60 fot two adults and three children to attend the same show. How much does it cost for one adult and one child to attend the show?

Answer 1

Answers:

It costs $15 for one adult

It costs $10 for one child

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Work Shown:

x = cost for one adult ticket (in dollars)

y = cost for one child ticket (in dollars)

"it costs $35 for one adult and two children" so the first equation is x+2y = 35. Solve for x to get x = -2y+35 (subtract 2y from both sides). We'll use this equation later. See the "replacement" step below.

"it costs $60 for two adults and three children" so the other equation to set up is 2x+3y = 60

Use the substitution rule to get rid of the x (replace it with something equivalent in terms of y) then isolate y

2x+3y = 60

2( x )+3y = 60

2( -2y+35 )+3y = 60 ... replace x with -2y+35

2(-2y)+2(35)+3y = 60

-4y+70+3y = 60

-y+70 = 60

-y+70-70 = 60-70

-y = -10

y = 10

Since y = 10, it costs $10 for one kid to get a ticket.

If y = 10, then x must be...

x = -2y+35

x = -2*10+35 ... replace y with 10

x = -20+35

x = 15

Since x = 15, it costs $15 for one adult ticket.