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.
Explanation: