Question

Samantha's mother spent $78 at a farmers market. She bought the same number of pounds of apples for $1.50 per lb as tomatoes for $2.50 per lb. She also bought half that weight of a farmers cheese that sold for $4.00 per lb. The number of pounds of peaches she bought for $3.00 per lb was one more pound than the farmers cheese. How many pounds of each product did Samantha's mother buy? Worth 85 points, this question.

Answer 1

Answer:

Let's define the data:

A = # of pounds of apples.

T = # of pounds of tomatoes

C = # of pounds of cheese

P = # of pounds of peaches.

The data we have is:

Total money spent = $78

Then we have the equations:

A*$1.50 + T*$2.50 + C*$4.00 + P$3.00 = $78

"She bought the same number of pounds of apples for $1.50 per lb as tomatoes for $2.50 per lb"

A = T

"She also bought half that weight of a farmer's cheese that sold for $4.00 per lb. "

C = T/2

"he number of pounds of peaches she bought for $3.00 per lb was one more pound than the farmer's cheese."

P =  C + 1 = T/2 + 1.

Then we can replace all our variables in the first equation, using the given data, then the first equation can be rewritten as:

T*$1.50 + T*$2.50 + (T/2)*$4.00 + (T/2 + 1)*$3.00 = $78

Now we can solve this for T.

T*( $1.50 + $2.50 + $4.00/2 ´+ $3.00/2) + $3.00 = $78

T*($7.50) = $78 - $3 = $75

T = $75/$7.50 = 10

Then she bought 10 pounds of tomatoes.

A = T = 10

She also bought 10 pounds of apples.

C = T/2 = 10/2 = 5

She bought 5 pounds of cheese.

P = C + 1 = 5 + 1 = 6

She bought 6 pounds of peaches.