Can you help me with this problem?

Question

Sergio has a mixture of Virginia peanuts and Spanish peanuts that he sales for $3.40 a pound. To make the mixture, he uses V peanuts that cost $3.50 per pound and S peanuts that cost $3.00 a pound. He mixes 10lbs at a time. How many pounds of V peanuts did he use? How many S peanuts did he use?

Answer 1

3.5v + 3s = 3.40 * 10
v + s = 10

s =10 - v

3.5v + 3(10 - v) = 34
3.5v + 30 - 3v = 34
3.5 v - 3v = 34 - 30
0.5v = 4
v = 8 lbs
s = 2 lbs

Answer 2

You need to state the problem more specifically. The way it is written he could put in 1 V peanut per 10lb bag and still sell them for $3.40/lb and make a handsome profit.

I assume that you really meant to say that he mixes them in a proportion such that $3.40/lb for 10lbs or $34.00 would be the price whether or not he sold the nuts mixed or separately.
If that is the case here is how you do it:

call x the weight in lbs of V nuts and y the weight of S nuts.

Then (x+y)3.40=34.00
also, x(3.50)+y(3.00)=34.00

Now multiply them out:

3.40x+3.40y=3.50x+3.00y
so

.40y=.10xor 4y=x

This tells us that for every lb of V nuts (x),there are 4 lbs of S nuts(y).

1/5 of the nuts are Spanish peanuts and 4/5 are of the Virginia variety. Since the total is 10 lbs that means he put 8 lbs of V and 2 lbs of S in each 10 lb bag.

To check your work, multiply out 8 lbs($3.50/lb) and add it to 2 lbs($3.00/lb). If these weights are correct you should get $34.00.

Your teacher may say that I have left out a step and she will be right. When I saw that 4y=x I could see right away what the weights would be. If the numbers are not so easy do this--
Go back to you original equation (x+y)3.40=34.00
Where you see x, substitute in 4y giving you (5y)3.40=34.00
5y=10
y=2 lbs.
Same answer, better form.

Answer 3

If v = the number of lbs. of V Peanuts, then 10-v is the number of lbs. of S peanuts. That leads us to this equation:

3.5(v) + 3(10-v)=3.4X10
3.5v+30-3v=34
.5v+30=34
.5v+30-30=34-30
.5v=4
v=8
10-v=2

He uses 8 pounds of V peanuts and 2 pounds of S peanuts to make each 10 pound batch of the mix.

Answer 4

It seems to me there is information missing from your question.

It would make sense though, that he would use more Spanish peanuts than Virginia peanuts because he is selling them for less than the higher priced peanuts.

Answer 5

That's a trick question that can't be answered with the information you gave. No one sells stuff at the same price that cost him to make it. What we need to know is what Sergio's markup is.

Answer 6

7x/2+3y=34
3x+3y=30
1/2x=4
x=8
he uses 8 lbs of V and 2 lbs of S

Answer 7

use a calculator.

Answer 8

3.5V+3S = 3.4X