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How many pounds of candy that sells for 
$1.25 per lb must be mixed with candy that sells for 
$0.75 per 
lb to obtain 
20lb of a mixture that should sell for 
$1.00 per 
lb ?

◻ Ib of 
$1.25-per-lb candy must be mixed with 
◻ lb of 
$0.75-per-lb candy.
(Type integers or decimals.)

How many pounds of candy that sells for $1.25 \$ 1.25 per lb must be mixed with candy that sells for $0.75 \$ 0.75 per lb \mathrm{lb} to obtain 20lb 20 \mathrm{lb} of a mixture that should sell for $1.00 \$ 1.00 per lb \mathrm{lb} ?\newline \square Ib of $1.25 \$ 1.25 -per-lb candy must be mixed with \square lb of $0.75 \$ 0.75 -per-lb candy.\newline(Type integers or decimals.)

Full solution

Q. How many pounds of candy that sells for $1.25 \$ 1.25 per lb must be mixed with candy that sells for $0.75 \$ 0.75 per lb \mathrm{lb} to obtain 20lb 20 \mathrm{lb} of a mixture that should sell for $1.00 \$ 1.00 per lb \mathrm{lb} ?\newline \square Ib of $1.25 \$ 1.25 -per-lb candy must be mixed with \square lb of $0.75 \$ 0.75 -per-lb candy.\newline(Type integers or decimals.)
  1. Define candy amounts: Let xx be the amount of $1.25\$1.25-per-lb candy, and (20x)(20 - x) be the amount of $0.75\$0.75-per-lb candy.
  2. Set up equation: Set up the equation based on the price per pound of the mixture: 1.25x+0.75(20x)=20×1.001.25x + 0.75(20 - x) = 20 \times 1.00.
  3. Simplify equation: Simplify the equation: 1.25x+150.75x=201.25x + 15 - 0.75x = 20.
  4. Combine like terms: Combine like terms: 0.50x+15=200.50x + 15 = 20.
  5. Subtract 1515: Subtract 1515 from both sides: 0.50x=50.50x = 5.
  6. Divide by 00.5050: Divide both sides by 00.5050 to find xx: x=50.50x = \frac{5}{0.50}.
  7. Calculate x: Calculate xx: x=10x = 10.

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