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How many pounds of candy that sells for 
$1.75 per lb must be mixed with candy that sells for 
$1.25 per 
lb to obtain 
20lb of a mixture that should sell for 
$1.50 per 
lb ?

◻ lb of 
$1.75-per-lb candy must be mixed with 
◻ lb of 
$1.25-per-lb candy.
(Type integers or decimals.)

How many pounds of candy that sells for $1.75 \$ 1.75 per lb must be mixed with candy that sells for $1.25 \$ 1.25 per lb \mathrm{lb} to obtain 20lb 20 \mathrm{lb} of a mixture that should sell for $1.50 \$ 1.50 per lb \mathrm{lb} ?\newline \square lb of $1.75 \$ 1.75 -per-lb candy must be mixed with \square lb of $1.25 \$ 1.25 -per-lb candy.\newline(Type integers or decimals.)

Full solution

Q. How many pounds of candy that sells for $1.75 \$ 1.75 per lb must be mixed with candy that sells for $1.25 \$ 1.25 per lb \mathrm{lb} to obtain 20lb 20 \mathrm{lb} of a mixture that should sell for $1.50 \$ 1.50 per lb \mathrm{lb} ?\newline \square lb of $1.75 \$ 1.75 -per-lb candy must be mixed with \square lb of $1.25 \$ 1.25 -per-lb candy.\newline(Type integers or decimals.)
  1. Define variables: Let xx be the pounds of $1.75\$1.75 candy, and (20x)(20 - x) be the pounds of $1.25\$1.25 candy.
  2. Set up equation: Set up the equation: 1.75x+1.25(20x)=1.50×201.75x + 1.25(20 - x) = 1.50 \times 20.
  3. Simplify equation: Simplify the equation: 1.75x+251.25x=301.75x + 25 - 1.25x = 30.
  4. Combine like terms: Combine like terms: 0.5x+25=300.5x + 25 = 30.
  5. Subtract and solve: Subtract 2525 from both sides: 0.5x=50.5x = 5.
  6. Calculate $1.25\$1.25 candy: Divide both sides by 0.50.5 to find xx: x=10x = 10.
  7. Calculate $1.25\$1.25 candy: Divide both sides by 0.50.5 to find xx: x=10x = 10.Calculate the pounds of $1.25\$1.25 candy: 20x=2010=1020 - x = 20 - 10 = 10.

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