What is the cost per pound of the wheat flour and of the rye flour.

Question

A baker purchased 15 lb of wheat flour and 13 lb of rye flour for a total cost of $19.05. A second purchase, at the same prices, included 11 lb of wheat flour and 10 lb of rye flour. The cost of the second purchase was $14.25. Find the cost per pound of the wheat flour and of the rye flour.

Answer 1

From this word problem, we can get two equations:

15w + 13r = 19.05 and 11w + 10r = 14.25

Let's rearrange the first to solve for w.

15w = 19.05 - 13r

w = 19.05/15 - 13/15 r

w = 1.27 - 0.87 r

Now substitute this equation for w into the second equation.

11 ( 1.27 - 0.87r ) + 10r = 14.25

Distribute the 11 into the parentheses.

11*1.27 - 11*0.87r + 10r = 14.25

13.97 - 9.57r + 10r = 14.25

Combine like terms

13.97 + 0.43r = 14.25

Solve for the price of r

0.43r = 14.25-13.97 = 0.28

r = 0.28/0.43

r = 0.65

The price of rye flour is $0.65 / lb

Now use this in the equation we found for wheat flour:

w = 1.27 - 0.87r

w = 1.27 - 0.87 * (0.65)

w = 1.27 - 0.57

w = 0.70

The price of wheat flour is $0.70 / lb