Help please

Question

Ellen wishes to mix candy worth $1.01 per pound with candy worth $2.62 per pound to form 30 pounds of a mixture worth $1.98 per pound. How many pounds of the more expensive candy should she use? Round the answer to the nearest pound. 

Answer 1

Hi Hillary, the way to solve mixture problems is to create a table of the information.

 

Let x be the pounds of $1.01 candy needed.

 

Then, 30 - x will be the pounds of $2.62 candy needed

 

Candy cost          Pounds                 Total

-------------------------------------------------------

$1.01                    x                   1.01 * x

 

$2.62                 30 - x               2.62 * (30 - x)

 

$1.98                   30                  1.98 * (30)

 

We know the total of the $1.01 candy plus total of the $2.62 candy must equal the total of the $1.98 candy.

 

Equation:

 

1.01 * x + 2.62 * (30 - x) = 1.98 * (30)

 

Multiply the entire equation by 100 to clear the decimals:

 

101x + 262 * (30 - x) = 198 * 30

 

Clear the parenthesis:

 

101x + 7860 - 262x = 5940

 

Combine terms:

 

-161x + 7860 = 5940

 

Add 161x to both sides:

 

7860 = 161x + 5940

 

Subtract 5940 from both sides:

 

161x = 1920

 

Divide both sides by 161:

 

x = 11.93, rounded to the nearest pound, x = 12

 

Ellen needs 12 pounds of the $1.01 candy.

 

Ellen needs 30 - 12, or 18 pounds of the $2.62 candy.

 

Questions?