Farmers market algebra

Question

At a farmers' market, Frederick buys 4 pounds of apples and 14 pounds of cherries for $40.66. At the same farmers' market, Wilhelmina buys 12 pounds of apples and 7 pounds of cherries for $29.93. Determine the price per pound of apples and cherries at the farmers' market. 

Answer 1

Let's use the variable, a, to represent the price of one pound of apples and the variable, c, to represent the price of one pound of cherries.

We can write the following equations to represent the two days sales amounts:

4a + 14c = $40.66

12a + 7c = 29.93

Now we can solve these two equations with two unknowns to find the price of each type of fruit.

Multiply the first equation by -3 to find the price of one pound of cherries:

4a + 14c = $40.66 becomes -12a - 42c = -121.98

Now combine this "new" equation with the second one:

-12a - 42c = -121.98

12a + 7c = 29.93

-35c = -92.05

c = $2.63

The price of one pound if cherries is $2.63.

Now substitute $2.63 for c in either of the original equations to find the price a of one pound of apples (Let's use the first equation.)

4a + 14c = 40.66

4a + 14 • 2.63 = 40.66

4a + 36.82 = 40.66

4a + 36.82 - 36.82 = 40.66 - 36.82

4a = 3.84

a = $0.96

The cost of one pound of apples is $0.96