Question

30pts for whoever answers this!!!

Solve the following problem. It may be helpful to use draw a chart on scrap paper to organize the information and write the equation. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit.

A grocer wants to make a 10-pound mixture of cashews and peanuts that he can sell for $3.64 per pound. If cashews cost $5.80 per pound and peanuts cost $2.20 per pound, how many pounds of each must he mix?

Answer 1

Let the weights of the cashews and peanuts be c and p respectively.  Then:

c + p = 10 lb.

The related cost equation is 5.80c + 2.20p = 3.64(c+p).

Because c + p = 10 lb,  the previous equation is equivalent to:

5.80c + 2.20p = 3.64(10)  =  36.40

Solving c + p for c, we get c = 10 - p.  Then, the last equation becomes:

5.80(10-p) + 2.20p = 36.40, or 58 - 5.8p = 36.4.  Solving for p:  

-5.8p = 36.4 - 58, or    -5.8p = -21.6.  Finally, p = 3.72 lb.

Since c + p = 10 (lb), c = 10-3.72 (lb), or   c = 6.28 lb.

He must make this 10-lb mixture as follows:  6.28 lb of cashews and 3.72 lb of peanuts.

Answer 2

We get cashews as variable x and peanuts as variable y

First equation is  x+y=10 => y= 10 - x

Second equation is 5.8x + 2.2y = 3.64 (x+y)

When we replace y in the second equation we get

5.8x + 2.2( 10-x ) = 3.64 * 10 => 5.8x + 22 - 2.2x = 36.4 =>

5.8x - 2.2x = 36.4 - 22 => 3.6x = 14.4 => x = 14.4/3.6 =4

x=4 when we replace x in the first equation we get y=6

He must mix 4 pounds of the cashews and 6 pounds of peanuts.

Good luck!!!