Question

Starting your trip in Georgia, 3 pieces of peach cobbler and 4 pieces of raspberry cobbler were purchased for breakfast for $18.00 and then 6 pieces of peach cobbler and 5 pieces of raspberry cobbler were purchased for lunch for $27.00. Determine the price for a piece of each type of cobbler.

A. Peach cobbler costs $3.00 per piece, and raspberry cobbler costs $2.00 per piece.
B. Peach cobbler costs $2.00 per piece, and raspberry cobbler costs $3.00 per piece.
C. Peach cobbler costs $4.00 per piece, and raspberry cobbler costs $5.00 per piece.
D. Peach cobbler costs $5.00 per piece, and raspberry cobbler costs $4.00 per piece.

Answer 1

By setting up simultaneous equations with the given transactions and solving them, we find that peach cobbler costs $2.00 per piece, and raspberry cobbler costs $3.00 per piece.

Step-by-step explanation:

To determine the price for a piece of peach cobbler and raspberry cobbler, let's set up two equations based on the information given. Let P represent the price per piece of peach cobbler and R represent the price per piece of raspberry cobbler.

From the first purchase, we have the equation: 3P + 4R = $18.00 (1)

From the second purchase, we have the equation: 6P + 5R = $27.00 (2)

To solve these equations simultaneously, one approach is to multiply the first equation by 2, so that the coefficient of P in both equations is the same:

2(3P + 4R) = 2($18.00)

6P + 8R = $36.00 (3)

Now, we subtract equation (2) from equation (3):

(6P + 8R) - (6P + 5R) = ($36.00 - $27.00)

3R = $9.00

R = $3.00 per piece of raspberry cobbler

Now, plug the value of R into equation (1):

3P + 4($3.00) = $18.00

3P + $12.00 = $18.00

3P = $18.00 - $12.00

3P = $6.00

P = $2.00 per piece of peach cobbler

Therefore, the correct answer is B. Peach cobbler costs $2.00 per piece, and raspberry cobbler costs $3.00 per piece.