SOLUTION: Here is the problem: Candy corn is $5 a pound and Good-N-Plenty is $7 a pound. Cindy wants 100 pounds of a mixture worth $5.44 a pound. How many pounds of each does she need?

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Here is the problem: Candy corn is $5 a pound and Good-N-Plenty is $7 a pound. Cindy wants 100 pounds of a mixture worth $5.44 a pound. How many pounds of each does she need?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 710524: Here is the problem:
Candy corn is $5 a pound and Good-N-Plenty is $7 a pound. Cindy wants 100 pounds of a mixture worth $5.44 a pound. How many pounds of each does she need?

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Put some variables into this and then create the suitable equations to solve.

L, the price of the cheaper candy, $5/pound
H, the price of the more expensive candy, $7/pound
T, the target price of the mixture of candies, %5.44/pound
u, how many pounds of the cheaper candy to use, unknown
v, how many pounds of the more expensive candy to use, unknown
M, the amount of mixed candy using the two (Candy Corn and Good-n-Plenty), 100 pounds

MAKING THE EQUATIONS
This will be the money divided by the mixture, equivalent to the target price per pound.

SYSTEM
%28uL%2BvH%29%2FM=T
u%2Bv=M

Various ways to solve that for u and v. Here, I'll use the second equation, solve it for u, then substitute this into the rational equation and solve for v.

Find first, u=M-v.
Now let's use the work at the rational equation.
uL%2BvH=MT
%28M-v%29L%2BvH=MT, just substituted for u.
ML-Lv%2BHv=MT
-Lv%2BHv=MT-ML
Hv-Lv=MT-ML
v%28H-L%29=M%28T-L%29
highlight%28v=M%28T-L%29%2F%28H-L%29%29, our first part of the solution, all in symbols.

Now, you could substitute the known values and find the value for v. Use the simpler relation, u=M-v to get the value for u.

The final numeric values answer for this one is highlight%28u=78%29 and highlight%28v=22%29, pounds of Candy Corn, and Good-N-Plenty, respectively for 100 pound mixture at $5.44/pound.