Answer:
1 pound of apple costs $2.50
1 pound of strawberries costs $1.25
Explanation:
System of Equations
Let's define the following variables:
x = cost of 1 pound of apples
y = cost of 1 pound of strawberries
.........................................
Marcus purchased 3 pounds of apples and 4 pounds of strawberries for a total of $12.50. Thus:
3x + 4y = 12.50 [1]
Shannon purchased 5 pounds of apples and 1 pound of strawberries for a total of $13.75, thus:
5x + y = 13.75 [2]
We need to solve the system of the equations [1] and [2].
Solving for y in [2]:
y = 13.75 - 5x [3]
Substituting in [1]
3x + 4(13.75 - 5x) = 12.50
Operating:
3x + 55 - 20x = 12.50
-17x = -55 + 12.50 = -42.50
Dividing by -17:
x = -42.50/(-17)
x = 2.5
Substituting in [3]:
y = 13.75 - 5*2.5
y = 1.25
Solution:
1 pound of apple costs $2.50
1 pound of strawberries costs $1.25