Question

A bagel shop charges a fee for delivery. On Thursday, three dozen bagels were delivered to an office at a total cost of $35. On Friday, four dozen bagels were delivered to a school at a total cost of $44. Which of the following is a viable solution to the system, where x is the cost of a dozen bagels and y is the delivery fee?(1 point)
Responses

(11,4)
left parenthesis 11 comma 4 right parenthesis

(10,5)
left parenthesis 10 comma 5 right parenthesis

(8,11)
left parenthesis 8 comma 11 right parenthesis

(9,8)

Answer 1

To solve the problem, we can set up a system of equations based on the information provided.

Let \( x \) be the cost of a dozen bagels and \( y \) be the delivery fee.

From the information given, we can formulate two equations:

1. For Thursday's delivery:
\[
3x + y = 35
\]
(since three dozen bagels were delivered at a total cost of $35)

2. For Friday's delivery:
\[
4x + y = 44
\]
(since four dozen bagels were delivered at a total cost of $44)

Next, we will solve this system of equations.

First, we can subtract the first equation from the second to eliminate \( y \):

\[
(4x + y) - (3x + y) = 44 - 35
\]

This simplifies to:

\[
4x - 3x = 9
\]

So we have:

\[
x = 9
\]

Now, we can substitute \( x \) back into one of the original equations to find \( y \). We'll use the first equation:

\[
3(9) + y = 35
\]

This simplifies to:

\[
27 + y = 35
\]

Subtracting 27 from both sides gives:

\[
y = 8
\]

Thus, we have determined that \( x = 9 \) and \( y = 8 \), which gives the solution \( (9, 8) \).

Therefore, the viable solution from the options provided is:

\[
\boxed{(9,8)}
\]