How many pounds of candy that sells for $0.71 per lb must be mixed with candy that sells for $1.25 per lb to obtain 8 lb....

Question

How many pounds of candy that sells for $0.71 per lb must be mixed with candy that sells for $1.25 per lb to obtain 8 lb of a mixture that should sell for $0.91 per lb? 

 

$0.71-per-lb candy: ___ lb 

(Type an integer or decimal rounded to two decimal places as needed.) 

Answer 1

Set the variables.

 

Let # of pounds for $0.71 = x

Let # of pounds for $1.25 = y

 

 

Set the equations.

 

x + y = 8      ----->       total pounds in mixture

 

0.71x + 1.25y = 0.91 * 8   ----->      total price of mixture

 

 

These are the two equations we will work with.

 

x + y = 8                                 eq1

0.71x + 1.25y = 7.28                 eq2

 

 

Multiply eq1 by 1.25.  Keep eq2. 

 

1.25x + 1.25y = 10                     eq1

0.71x + 1.25y = 7.28                  eq2

 

 

Subtract eq2 from eq1 to eliminate the y terms.

 

 

0.54x = 2.72

 

     x = 5.04

Answer 2

Step 1: Identify variables.

Let x = # lbs of $0.71/lb candy

Let y = # lbs of $1.25/lb candy

 

Step 2: Set up equations. Since there are 2 variables, we need at least 2 equations.

Final mixture is a total of 8 lbs, so EQ 1: x + y = 8

Selling price is $0.91/lb, so EQ 2: .71x + 1.25y = .91(8)

 

Step 3: Use substitution or elimination methods for solving systems of equations.  For this problem, I will show the substitution method by using EQ 1 to solve for y in terms of x.

 

EQ 1: x + y =8

y = 8 - x

 

EQ 2: .71x + 1.25y = .91(8)

.71x + 1.25(8 - x) = 7.28

.71x + 10 - 1.25x = 7.28

-.54x = -2.72

x = 5.037... = 5.04lb

 

Usually, the next step would be to plug x into one of the equations and solve for y, but since this question is asking for the number of lbs of $0.71/lb candy that is in the mix (which we defined to be x), we can stop here.  The answer is 5.04lbs.

 

Hope this was helpful!

 

~Patty S.

Answer 3

Let X be the amount of the cheaper candy and 8-X be the amount of the more expensive candy. This totals 8 lb. of candy.

 

The mixture costs a total $ [0.71X+1.25(8-X)] and this must be (8 lb)($0.91/lb) = $7.28.

 

Now equate and solve for X.

 

0.71X + 1.25(8-X) = 7.28

 

0.71X + 10 - 1.25X = 7.28

 

-0.54X = -2.72

 

X = 2.72 / 0.54  ≈ 5.04

 

8 - X ≈ 8 - 5.04 = 2.96

 

You need about 5.04 lb of the $0.71/lb candy, and 2.96 lb of the $1.25/lb candy.