Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many pounds of candy that sells for 
$3.25 per lb must be mixed with candy that sells for 
$1.75 per 
lb to obtain 
20lb of a mixture that should sell for 
$2.50 per lb?

◻ Ib of 
$3.25-per-lb candy must be mixed with 
◻ Ib of 
$1.75-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 $1.75 \$ 1.75 per lb \mathrm{lb} to obtain 20lb 20 \mathrm{lb} of a mixture that should sell for $2.50 \$ 2.50 per lb?\newline \square Ib of $3.25 \$ 3.25 -per-lb candy must be mixed with \square Ib of $1.75 \$ 1.75 -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 $1.75 \$ 1.75 per lb \mathrm{lb} to obtain 20lb 20 \mathrm{lb} of a mixture that should sell for $2.50 \$ 2.50 per lb?\newline \square Ib of $3.25 \$ 3.25 -per-lb candy must be mixed with \square Ib of $1.75 \$ 1.75 -per-lb candy. (Type integers or decimals.)
  1. Define variables: Let xx be the pounds of $3.25\$3.25-per-lb candy, and (20x)(20 - x) be the pounds of $1.75\$1.75-per-lb candy.
  2. Set up equation: Set up the equation based on the total cost of the mixture: 3.25x+1.75(20x)=2.50×203.25x + 1.75(20 - x) = 2.50 \times 20.
  3. Distribute and simplify: Distribute and simplify the equation: 3.25x+351.75x=503.25x + 35 - 1.75x = 50.
  4. Combine like terms: Combine like terms: 1.5x+35=501.5x + 35 = 50.
  5. Subtract 3535: Subtract 3535 from both sides: 1.5x=151.5x = 15.
  6. Divide by 11.55: Divide both sides by 11.55 to solve for xx: x=151.5x = \frac{15}{1.5}.
  7. Calculate x: Calculate xx: x=10x = 10.

More problems from Weighted averages: word problems