How many pounds of candy that sells for $0.89 per lb must be mixed with candy that sells for $1.31 per lb to obtain 9 lb of a mixture that should sell for $0.95

Question

How many pounds of candy that sells for $0.89 per lb must be mixed with candy that sells for $1.31 per lb to obtain 9 lb of a mixture that should sell for $0.95 per lb?

Answer 1

The question seems a bit confusing, but I think I've figured out what they're looking for. It's $0.95/lb of the candy mixture, and so how many pounds of each candy do you have in a 9 lb. mix? This is what I've done...

 

Alright, here's what we know:

0.89*c+1.31*m=0.95

c+m=1

1) c+m=9   I need to subtract m from both sides 

    c+m-m+9-m

    c=1-m

 

2) I will substitute (9-m) in for c in the top equation so....

    0.89*(1-m)+1.31*m=0.95

 

3) Now i'm left with an equation to work out. I'm solving for m.

    0.89*(1-m)+1.31*m=0.95

    0.89-0.89*m +1.31*m=0.95

    

    I want to combine like terms, so I can add the 2 m's up.

    0.89+0.42*m=0.95

 

    I want to get the variable (m) by itself, so I know how much it is. I need to use the order of operations.

    0.89+0.42*m=0.95

      -0.89           -0.89

    0.42*m=0.06

    0.42*m/0.42=0.06/0.42

    m=0.06/0.42

    m=(rounded)0.14286  or...

    m=(not rounded) 1/7 lb.

 

4) if m=1/7 lb, then we can solve the 2nd equation for c

    c+m=1

    c+1/7=1  (whatever we do to one side, we do to the other!)

      -1/7   -1/7

    c=1-1/7

    c=6/7 

 

5) So, 6/7 of the 9 lb. mixture is worth $0.89/1 lb, and 1/7 of the 9 lb. mixture is worth $1.31/1 lb. 

    9 lbs * 6/7 = about 7.71 lbs

    9 lbs * 1/7 = about 1.29 lbs

 

There you go. Let me know if I this helps!

 

    

Answer 2

 

Hi Faith,

 

- Candy A: $0.89/lb, x lb to obtain 9 lb of a mixture that should sell for $0.95

 

- Candy B: $1.31/lb, y lb to obtain 9 lb of a mixture that should sell for $0.95

 

Then, from the weight perspective

 

     x + y = 9                         (Eq. 1)

 

From the price perspective

 

     0.89x + 1.31y = 0.95 · 9

 

     0.89x + 1.31y = 8.55       (Eq. 2)

 

Solving the system of Eq. 1 and Eq. 2, we get

 

     x = 7.71 lb (candy A),   y = 1.29 lb (candy B)