SOLUTION: Please help me!!!! A store is selling two different types of cheese. One type sells for $3.75 a pound and a second type sells for $4.55 a pound. How many pounds of the $3.75 ch

Question 704816: Please help me!!!!
A store is selling two different types of cheese. One type sells for $3.75 a pound and a second type sells for $4.55 a pound. How many pounds of the $3.75 cheese would the store need to mix together with the $4.55 cheese to get a 45-pound block mixture that sells for $4.05 a pound?

Thank you so much! :D

Found 3 solutions by stanbon, Stitch, josmiceli:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A store is selling two different types of cheese. One type sells for $3.75 a pound and a second type sells for $4.55 a pound. How many pounds of the $3.75 cheese would the store need to mix together with the $4.55 cheese to get a 45-pound block mixture that sells for $4.05 a pound?
------
Equations:
a + b = 45 lbs
375a + 455b = 405*45
------
455a + 455b = 455*45
375a + 455b = 405*45
-------
80a = 50*45
a = (5/8)45
a = 28.125 lbs (amt. of $3.75 cheese needed)
===============
Cheers,
Stan H.
Answer by Stitch(470)   (Show Source): You can put this solution on YOUR website!
Let A = pounds of cheese that costs $3.75/pound
Let B = pounds of cheese that costs $4.55/pound
Equation 1: (A 45 pound block of mixed cheese)
Equation 2: (The cost per pound of the mixed cheese block)
------------------------------------------
Solve Equation 1 for one of the variables.
Equation 1:

Now plug (45 - B) into Equation 2 for A
Equation 2:

Multiply the 3.75 trough and simplify the equation

Multiply both sides by 45

Combine like terms

Subtract 168.75 from both sides

Divide both sides by 0.8

Now plug 16.875 into equation 1 for B
Equation 1:

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = pounds of the $3.75/pound cheese needed
Let = pounds of the $4.55/pound cheese needed
given:
(1)
(2)
--------------------------------
(2)
(2)
(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)

and, since
(1)
(1)
(1)
(1)
28.125 pounds of the $3.75/pound cheese is needed
16.875 pounds of the $4.55/pound cheese is needed
check answer:
(2)
(2)
(2)
(2)
(2)
OK

RELATED QUESTIONS
A candy store sells candy in bulk. In one bin are sour worms which sells for $2.20 per... (answered by josmiceli)
Please help me solve this word problem: A computer store sells two different types of... (answered by checkley77)
The Candy Emporium sells two types of hard candy--type A sells for $1.50 per pound and... (answered by mananth)
The Candy Emporium sells two types of candy- type A sells for $1.50 per pound and type B... (answered by stanbon)
A cand store has two types of jelly beans, one selling for $3 per pound and the other... (answered by josgarithmetic)
A deli has five types of meat,two types of cheese,and three types of bread.how many... (answered by ewatrrr)
1.) A store sells one type of candy for 4.00 per pound and another type for 10.00 per... (answered by josgarithmetic)
Use two equations in two variables to solve the problem. A coffee supply store waits... (answered by josgarithmetic)
A candy store has two types of jelly beans, one selling for $2 per pound and the other... (answered by mananth)