word problem solving with two unknowns, using rate(time)=distance?

Question

A baker purchased 12lbs of wheat flour and 15lbs of rye flour for a total cost of $18.30. A second purchase, at the same prices, included 15 lbs of wheat flour and 10lbs of rye flour. The cost of the second purchase was $16.75. Find the cost per pound of the wheat flour and of the rye flour.

Answer 1

Let w = price of wheat flour per pound
Let r = price of rye flour per pound

First we have to set up our system of equations.
12w + 15r = 18.30
15w + 10r = 16.75

Now we will use substitution to solve for a variable.
12w + 15r = 18.30
Subtract 12w from both sides.
15r = 18.30 - 12w
Divide both sides by 15.
r = 1.22 - .8w

Now we substitute r into the other equation.
15w + 10r = 16.75
15w + 10 (1.22 - .8w) = 16.75
15w + 12.2 - 8w = 16.75
7w + 12.2 = 16.75
7w = 4.55
w = .65

Now we substitute w back into one of the equations to get r.
12w + 15r = 18.30
12(.65) + 15r = 18.3
7.8 + 15r = 18.3
15r = 10.5
r = .7

So, wheat flour costs $0.65 per pound and rye flour costs $0.70 per pound.

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Now we can check our answer in the other equation.

15w + 10r = 16.75
15(.65) + 10(.7) = 16.75
9.75 + 7 = 16.75
16.75 = 16.75

We are good! :)

Answer 2

Wheat Flour is 65cents/lb
Rye Flour is 70cents/lb

Answer 3

.65 cents
and
.70 cents

here's ur equations:
12X + 15Y = 18.3
solve for one of the variables and plug that into the second equation.
Which would be:
15X + 10Y = 16.75

Answer 4

12w+15r=18.30

15w+10r=16.75

rearrange one equation to get one of the variables and plug it back into the other equation.

.65 and .70 per pound

Answer 5

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