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How many pounds of candy that sells for 
$2.75 per lb must be mixed with candy that sells for 
$1.25 per 
lb to obtain 
10lb of a mixture that should sell for 
$2.45 per Ib?

◻ Ib of 
$2.75-per-lb candy must be mixed with 
◻ Ib of 
$1.25-per-lb candy.
(Type integers or decimals.)

How many pounds of candy that sells for $2.75 \$ 2.75 per lb must be mixed with candy that sells for $1.25 \$ 1.25 per lb \mathrm{lb} to obtain 10lb 10 \mathrm{lb} of a mixture that should sell for $2.45 \$ 2.45 per Ib?\newline \square Ib of $2.75 \$ 2.75 -per-lb candy must be mixed with \square Ib of $1.25 \$ 1.25 -per-lb candy.\newline(Type integers or decimals.)

Full solution

Q. How many pounds of candy that sells for $2.75 \$ 2.75 per lb must be mixed with candy that sells for $1.25 \$ 1.25 per lb \mathrm{lb} to obtain 10lb 10 \mathrm{lb} of a mixture that should sell for $2.45 \$ 2.45 per Ib?\newline \square Ib of $2.75 \$ 2.75 -per-lb candy must be mixed with \square Ib of $1.25 \$ 1.25 -per-lb candy.\newline(Type integers or decimals.)
  1. Define variables: Let xx be the amount of $2.75\$2.75-per-lb candy, and (10x)(10 - x) be the amount of $1.25\$1.25-per-lb candy.
  2. Set up equation: Set up the equation: 2.75x+1.25(10x)=2.45×102.75x + 1.25(10 - x) = 2.45 \times 10.
  3. Combine terms: Distribute and combine like terms: 2.75x+12.51.25x=24.52.75x + 12.5 - 1.25x = 24.5.
  4. Solve for x: Combine x terms: 1.5x+12.5=24.51.5x + 12.5 = 24.5.
  5. Substitute xx: Subtract 12.512.5 from both sides: 1.5x=121.5x = 12.
  6. Substitute xx: Subtract 12.512.5 from both sides: 1.5x=121.5x = 12.Divide both sides by 1.51.5 to solve for xx: x=121.5x = \frac{12}{1.5}.
  7. Substitute xx: Subtract 12.512.5 from both sides: 1.5x=121.5x = 12.Divide both sides by 1.51.5 to solve for xx: x=121.5x = \frac{12}{1.5}.Calculate xx: x=8x = 8.
  8. Substitute xx: Subtract 12.512.5 from both sides: 1.5x=121.5x = 12.Divide both sides by 1.51.5 to solve for xx: x=121.5x = \frac{12}{1.5}.Calculate xx: x=8x = 8.Substitute xx back into (10x)(10 - x) to find the amount of 12.512.500-per-lb candy: 12.512.511.

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