Question 245815
I will solve the candy problem. Start with what you know.
x = candy @ $1.80/lb
y = candy @ $2.40/lb
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She wants to produce 48 lbs valued at $2.00/lb.
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So we have x(1.80) + y(2.40) = 48(2.00) = 96.
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But with only one equation, having two unknowns is not solvable. But since we know the total, we define x in terms of y or y in terms of x.
x lb = 48 lb - y lb
y lb = 48 lb = x lb
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Rewriting the equation we have:
1.8x + 2.4y = 96
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Substitute y = 48-x
1.8x + 2.4(48-x) = 96
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Multiply thru
1.8x + 115.2 - 2.4x = 96
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Collect terms
-0.6x + 115.2 = 96
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Subtract 115.2 from both sides
-0.6x = 96 - 115.2 = -19.2
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Multiply both sides by -10
6x = 192
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Divide both sides by 6
x = 32
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Looking back to our setup, we know that y = 48-x = 48-32 = 16.
So we have 32 lb @ $1.80/lb =  $57.60
And we have 16 lb @ $2.40/lb = $38.40
Thus we have a total of 48 lb and a total cost of $57.60 + $38.40 = $96.00.
96/48 = $2/lb.
48 lb @ $2/lb = $96.
So our solution checks.
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