Question

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A group of eight friends went ice skating. Together, they paid $75.95 for admission and food while at the ice skating rink. Admission is $3.25 with a coupon and $5.50 without the coupon. The total cost of the food for all eight people was $36.45. How many people paid with the coupon and how many paid without the coupon?

Answer 1

Answer:

2 people paid with a coupon.

6 people paid full price with no coupon.

Step-by-step explanation:

We are going to subtract to find out how much money was paid for tickets to get in.

Total - Food = Tickets

see image.

There are 8 people so let

x = coupon people

y = no coupon people

x + y = 8

Coupon people only paid 3.25 so in total coupon-ers paid 3.25x

No coupon people paid 5.50y

3.25x + 5.50y = 39.50

see image.

Answer 2

Answer:

2 people paid with a coupon.

6 people paid without a coupon.

Step-by-step explanation:

Given information:

• Number of friends = 8
• Total paid for admission and food = $75.95
• Cost of admission with a coupon = $3.25
• Cost of admission without a coupon = $5.50
• Total cost of the food for all eight people = $36.45

Define the variables:

• Let x be the number of friends who used a coupon.
• Let y be the number of friends who did not use a coupon.

Subtract the total cost of the food from the total paid to determine the total amount paid for admission:

$\implies 75.95-36.45 = 39.50$

Create a system of equations with the given information and defined variables:

$\begin{cases}x + y = 8\\3.25x+5.50y=39.50\end{cases}$

Rearrange the first equation to make y the subject:

$\implies y=8-x$

Substitute the found expression for y into the second equation and solve for x:

$\implies 3.25x+5.50(8-x)=39.50$

$\implies 3.25x+44-5.50x=39.50$

$\implies -2.25x=-4.50$

$\implies x=2$

Substitute the found value of x into the first equation and solve for y:

$\implies 2+y=8$

$\implies y=6$

Solution:

• 2 people paid with a coupon.
• 6 people paid without a coupon.