SOLUTION: How many pounds of hamburger that costs $1.10 per pound must be mixed with 50 pounds of hamburger that costs $1.80 per pound to make a mixure that costs $1.30 per pound. I can

Question 116746: How many pounds of hamburger that costs $1.10 per pound must be mixed with 50 pounds of hamburger that costs $1.80 per pound to make a mixure that costs $1.30 per pound.
I can get the answer by working it out but can't get the correct equation down on paper.
Found 3 solutions by scott8148, checkley71, bucky:
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
let x="pounds of $1.10"

x(1.1)+50(1.8)=(x+50)(1.3) ___ 1.1x+90=1.3x+65 ___ 25=.2x
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
1.10*X+50*1.80=1.30(X+50)
1.10X+90=1.30X+65
1.10X-1.30X=65-90
-.20X=-25
X=-25/-.20
X=125 POUNDS OF $110 HAMBERG IS NEEDED.
PROOF:
1.10*125+50*1.80=1.30(125+50)
137.5+90=1.3(175)
227.5=227.5

Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
Let x be the unknown number of pounds of meat at $1.10 per pound that will be added to the
mix.
.
The net worth of this meat will be the cost per pound times the number of pounds to be added.
So the total cost of this meat will be 1.10*x.
.
For the other meat in the mix you have 50 pounds and it is priced at $1.80 per pound. So
this meat is worth 50 pounds times $1.80 per pound or 90 dollars.
.
The total amount of meat in the mix will be the total of x pounds plus 50 pounds ... an amount
equal to (50 + x) pounds. Since this meat is to be worth $1.30 per pound, the dollar amount
of the mixed meat will be its weight (50 + x pounds) times $1.30 per pound.
.
Now we can write a cash based equation. The dollar amount of the $1.10 meat plus the dollar
amount of the $1.80 meat must equal the dollar amount of the mixed meat. In equation form
this is:
.
1.10*x + 50*1.80 = (50 + x)* 1.30
.
Multiplying 50*1.8 gives 90 and this makes the equation become:
.
1.10x + 90 = (50 + x)*1.30
.
Doing the distributed multiplication on the right side makes the equation:
.
1.10x + 90 = 50*1.30 + 1.30x
.
and 50 times 1.30 equals 65 which makes the equation:
.
1.10x + 90 = 65 + 1.30x
.
Get rid of the 90 on the left side by subtracting 90 from both sides:
.
1.10x = -25 +1.30x
.
Get rid of the 1.30x on the right side by subtracting 1.30x from both sides:
.
-0.2x = -25
.
Solve for x by dividing both sides by -0.2 and you get:
.
x = 125
.
This tells you that you add 125 pounds of meat that costs $1.10 per pound to 50 pounds of
meat that costs $1.80 per pound and you get 175 pounds (50 + 125) of meat that is worth $1.30
per pound.
.
Check: 125 pounds of meat at $1.10 per pound is 125*1.10 = $137.50. And 50 pounds of meat
at $1.80 per pound is the $90 that we previously found. So the two groups of meat are worth
a total of $137.50 + $90.00 = $227.50.
.
This makes 175 pounds of meat that is intended to be sold for $1.30 per pound. 175 times 1.30 = $227.50
.
So the mixed meat is worth the same as the sum of the two individual amounts of meat ... the
answer checks. And the answer is 125 pounds of meat worth $1.10 per pound.
.
Hope this helps you to understand the problem.
.
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