Question

A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?

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help?

Answer 1

you dont need to give me the answer Ive had this question before , just set me up alittle please

Answer 2

So the total cost of all of the nuts after they are mixed will be:

Tcost = 10 * 4.75 = 47.50

It will be comprised of peanuts and cashews such that:
4.00 * (x nuts) + 6.50 * (y cashews)

This mixture will equal the Total cost.

Answer 3

The other thing to think about is the relative cost of nuts and cashews. That's the final piece of the puzzle.

Cashews = Nuts + 2.50. (or y = x+2.5).

Answer 4

so he would want 5 pounds of both , for a 10 pound mixture right ?

Answer 5

hold up nevermind. Im wrong

Answer 6

So, we have:

Tcost = 47.50
4 * x + 6.5 * y = 47.5
and y = x + 2.5

So, solve:
4 * x + 6.5 * (x + 2.5) = 47.5

Answer 7

Simplifying:
4x + 6.5x + 16.25 = 47.5
10.5x = 31.25
x = 2.98 pounds.
Then y = x + 2.5
y = 5.47 pounds.

Answer 8

okay, so what does y equal exactly you never explained. 5.75 pounds is an answer option. So does that represent the number of peanuts? therefore I would subtract that from 10 pounds to get my number of cashews?

Answer 9

isn't*

Answer 10

I'm sorry, Renee..

The other part of what we needed to know is exactly what you said (x + y = 10.0)

So, instead of x+2.5 = y... use y = 10 - x...

This gives instead....
4x + 6.5(10-x) = 47.50

Answer 11

Sorry, I keep getting disconnected here at work. lol

Answer 12

so it would be 4x+ 65-6.5x=47.50 ?

Answer 13

65-2.5x=47.50
I mean

Answer 14

Right!
x - 7
y = 10 - x = 10 - 7 = 3!

Answer 15

thank you !

Answer 16

You're welcome. Have a great morning.