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How many pounds of candy that sells for 
$3.25 per lb must be mixed with candy that sells for 
$2.75 per lb to obtain 
20lb of a mixture that should sell for 
$3.15 per 
lb ?

◻ Ib of 
$3.25-per-lb candy must be mixed with 
◻ Ib of 
$2.75-per-lb candy. (Type integers or decimals.)

How many pounds of candy that sells for $3.25 \$ 3.25 per lb must be mixed with candy that sells for $2.75 \$ 2.75 per lb to obtain 20lb 20 \mathrm{lb} of a mixture that should sell for $3.15 \$ 3.15 per lb \mathrm{lb} ?\newline \square Ib of $3.25 \$ 3.25 -per-lb candy must be mixed with \square Ib of $2.75 \$ 2.75 -per-lb candy. (Type integers or decimals.)

Full solution

Q. How many pounds of candy that sells for $3.25 \$ 3.25 per lb must be mixed with candy that sells for $2.75 \$ 2.75 per lb to obtain 20lb 20 \mathrm{lb} of a mixture that should sell for $3.15 \$ 3.15 per lb \mathrm{lb} ?\newline \square Ib of $3.25 \$ 3.25 -per-lb candy must be mixed with \square Ib of $2.75 \$ 2.75 -per-lb candy. (Type integers or decimals.)
  1. Define Variables: Let xx be the amount of $3.25\$3.25-per-lb candy, and (20x)(20 - x) be the amount of $2.75\$2.75-per-lb candy.
  2. Set Up Equation: Set up the equation: 3.25x+2.75(20x)=3.15×203.25x + 2.75(20 - x) = 3.15 \times 20.
  3. Simplify Equation: Simplify the equation: 3.25x+552.75x=633.25x + 55 - 2.75x = 63.
  4. Combine Like Terms: Combine like terms: 0.5x+55=630.5x + 55 = 63.
  5. Subtract 5555: Subtract 5555 from both sides: 0.5x=80.5x = 8.
  6. Divide by 00.55: Divide both sides by 00.55 to find xx: x=80.5x = \frac{8}{0.5}.
  7. Calculate x: Calculate xx: x=16x = 16.
  8. Find $2.75\$2.75 Candy: Find the amount of $2.75\$2.75-per-lb candy: 20x=201620 - x = 20 - 16.
  9. Calculate $2.75\$2.75 Candy: Calculate the amount of $2.75\$2.75-per-lb candy: 2016=420 - 16 = 4.

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