Question

Stephen goes to the fair and buys two funnel cakes and one drink. His total bill is $6.75. A few days later, he goes with a friend and buys three funnel cakes and two drinks. This time his total bill is $11.

Write two equations that could be used to determine how much each funnel cake and drink costs. Use f for the cost of a funnel cake and d for the cost of a drink.

What is the cost of a funnel cake?

What is the cost of a drink?

Answer 1

Let's define the variables:

f = Cost per cake

d = Cost per drink.

"Stephen goes to the fair and buys two funnel cakes and one drink. His total bill is $6.75. "

2*f + 1*d = $6.75

"A few days later, he goes with a friend and buys three funnel cakes and two drinks. This time his total bill is $11."

3*f + 2*d = $11.

Then we have a system of equations:

2*f + 1*d = $6.75

3*f + 2*d = $11.

To solve this, the first step is to isolate one of the variables in one of the equations, let's isolate d in the first equation:

d = $6.75 - 2*f

Now we can replace this in the other equation:

3*f + 2*($6.75 - 2*f) = $11

3*f - 4*f + $13.50 = $11

-f = $11 - $13.50 = -$2.50

f = $2.50

Then the cost of a funnel cake is $2.50

And the cost of a drink can be obtained with the equation:

d = $6.75 - 2*f = $6.75 - 2*$2.50 = $1.75

The cost of a drink is $1.75