Compare Solution Methods for Multi-Step Equations Quick Check
5 of 55 of 5 Items
Question
Three adult and three child movie tickets were purchased for $75. The cost of each child ticket is $3 less than the cost of an adult ticket. Find the price of each ticket.(1 point)
Let's let x be the cost of an adult ticket and y be the cost of a child ticket.
We know that the cost of each child ticket is $3 less than the cost of an adult ticket, so we can write the equation y = x - 3.
We also know that three adult and three child movie tickets were purchased for $75. The cost of the adult tickets can be written as 3x since three adult tickets were purchased. The cost of the child tickets can be written as 3y since three child tickets were purchased. This can be combined into the equation 3x + 3y = 75.
Now we have a system of two equations:
y = x - 3
3x + 3y = 75
One way to solve this system of equations is by substitution. We can solve the first equation for y in terms of x:
y = x - 3
Now substitute this expression for y in the second equation:
3x + 3(x - 3) = 75
Simplify:
3x + 3x - 9 = 75
Combine like terms:
6x - 9 = 75
Add 9 to both sides:
6x = 84
Divide both sides by 6:
x = 14
Now we can substitute the value of x back into the first equation to find y:
y = 14 - 3
y = 11
So the price of an adult ticket is $14 and the price of a child ticket is $11.