word problems help

Question

A trail mix comprised of 59% raisins is being mixed with a trail mix variety that is 41% raisins to create a 72 lb. bag of trail mix that is 50% raisins.
How many pounds of the 59% raisins trail mix must be used?

Answer 1

x = lbs of 59% raisins

y = lbs of 41% raisins

 

x+y = total weight = 72 lbs

x = 72-y

0.59x + 0.41y = (0.5)(72)

0.59(72-y) + 0.41y = 36

42.48 - 0.59y + 0.41y = 36

-0.18y = -6.48

y = 36 = lbs of 41% raisins

x = 72 -36 = 36 lbs of 59% raisins

 

This problem can also be done by a method known as allegation (google it)

HAVE......WANT......NEED

59%.........................9...

...............50%..............

41%.........................9...

 

So, you need 9 parts of each, and since the total parts is 18 and that represents the total weight of 72 lbs, each part is equal to 72/18 = 4.  Thus, 9x4 = 36 so you need 36 labs of each.

Answer 2

r represents the 59% raisins

0.59r + 0.41(72 - r) = 0.50(72)

 

Can you solve for r and answer?

Answer 3

let x = the number of lb. of the 59% raisin mix

 

y = the number of lb. of the 41% raisin mix

 

x + y = 72

 

0.59x + 0.41y = 72(0.50) = 36

 

59x + 41y = 3600      if you multiply both sides of the above equation by 100 to clear the decimals

 

Solve x + y = 72  for  y

 

y = 72 -x

 

Put the above value of x into the second equation:

 

59x + 41(72 - x) = 3600

 

Solve the above linear equation for x to obtain the answer to the problem