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How many pounds of candy that sells for 
$3.25 per lb must be mixed with candy that sells for 
$2.75perlb to obtain 
10lb of a mixture that should sell for 
$2.90 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 $2.75perlb \$ 2.75 \mathrm{per} \mathrm{lb} to obtain 10lb 10 \mathrm{lb} of a mixture that should sell for $2.90 \$ 2.90 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.\newline(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 $2.75perlb \$ 2.75 \mathrm{per} \mathrm{lb} to obtain 10lb 10 \mathrm{lb} of a mixture that should sell for $2.90 \$ 2.90 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.\newline(Type integers or decimals.)
  1. Define Variables: Let xx be the amount of $3.25\$3.25-per-lb candy, and (10x)(10 - x) be the amount of $2.75\$2.75-per-lb candy.
  2. Set Up Equation: Set up the equation based on the total cost of the mixture: 3.25x+2.75(10x)=2.90×103.25x + 2.75(10 - x) = 2.90 \times 10.
  3. Combine Terms: Distribute and combine like terms: 3.25x+27.52.75x=293.25x + 27.5 - 2.75x = 29.
  4. Combine xx Terms: Combine the xx terms: 0.5x+27.5=290.5x + 27.5 = 29.
  5. Subtract Constants: Subtract 27.527.5 from both sides: 0.5x=1.50.5x = 1.5.
  6. Solve for x: Divide both sides by 0.50.5 to solve for x: x=3x = 3.

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