A baker purchased 13 lb of wheat flour and 15 lb of rye flour for a total cost o

Question

A baker purchased 13 lb of wheat flour and 15 lb of rye flour for a total cost of $22.50. A second purchase, at the same prices, included 19 lb of wheat flour and 12 lb of rye flour. The cost of the second purchase was $24.45. Find the cost per pound of the wheat flour and of the rye flour.

STEP 1: Let x represent the cost of wheat flour. Let y represent the cost of rye flour. Write an equation using x and y that describes the first purchase. x + 15 y = (Equation 1)

Write an equation using x and y that describes the second purchase. x + 12 y = (Equation 2)

STEP 2: Find the least common multiple of 15 and 12.

STEP 3: Multiply each equation you found in Step 1 by an appropriate constant to force the coefficient on y to be equal to the least common multiple of 15 and 12 in each case.

x + y = (Equation 3)

x + y = (Equation 4)

STEP 4: Subtract your result for Equation 4 in Step 3 from your result for Equation 3.

This eliminates the variable y. x =

STEP 5: Solve your result from Step 4 for x. x =

STEP 6: Substitute in the value for x you found in Step 5 into one of the original equations, and solve for y. y =

STEP 7: Express your results in terms of the original problem. The cost of the wheat flour is dollars per pound. The cost of the rye flour is dollars per pound.

Explanation / Answer

STEP 1: Let x represent the cost of wheat flour. Let y represent the cost of rye flour. Then 13x + 15 y = 22.50(Equation 1)

Also, as per the description of the second purchase, 19 x + 12 y = 24.45 (Equation 2)

STEP 2: The least common multiple of 15 and 12 is 60.

STEP 3: Multiply equation 1 by 4 and equation 1 by 5 .Then

52x +60 y =   90 (Equation 3) and

95x +60 y =   122.25(Equation 4)

STEP 4: Subtract Equation 3 in from Equation 4. Then 95x +60 y –(52x +60 y) = 122.25- 90 or, 95x -52x = 32.25 or, 43x = 32.25

STEP 5: x =32.25/43 = 0.75

STEP 6: on substituting x = 0.75 in equation 1, we get 13*0.75 + 15y = 22.5, or, 9.75 + 15y = 22.5 or, 15y = 22.5-9.75 or, 15y = 12.75 so that y = 12.75/15 = 0.85

STEP 7: The cost of the wheat flour is $ 0.75 per pound. The cost of the rye flour is $ 0.85 per pound.

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