Merchant mixed nuts worth 50 cents per lb with nuts worth 80 cents per lb. He wants to make a mix of 30 lbs?

Question

to sell at 75 cents per lb, how many pounds of each should he use?

I hav eno idea.

Answer 1

Ok here's how you work this. In this equation, x & y represent pounds of nuts.

You know that $.50(x) +$.80(y) = .75(x+y)

This is saying that 50 cents time x plus 80 cents times y will equal 75 cents times all the pounds of nuts.

You also know that x + y = 30 because the total lbs of nuts must be 30.

Because x & y are both pounds of nuts, they are interchangeable in both equations.

First, you have to one equation for either x or y.

I decided to solve the first equation for y.

.50x + .80y=.75(x+y)
.50x + .80y=.75x + .75y
.80y=.75x + .75y - .50x
.80y=.25x + .75y
.80y-.75y=.25x
.05y=.25x
y=5x

To solve the other equation, I chose to solve it for x.

x+y=30
x=30-y

Now we take the first equation and put in what we know for x; that it equals 30-y

So y=5(x)
y=5(30-y)
y=150-5y
y+5y=150
6y = 150
y = 25

Now that we know the value of y, we can substitute it into the other equation. The simplest is x=30-y

x=30-25
x=5

So your final answer is y=25 and x = 5

I took a picture of my work and posted it online if you want to see it.

http://fly.hiwaay.net/~mesa/math_problem.jpg

You can also check your work by substituting the values for x & y into either equation. To be safe, substitute them in both.

Answer 2

Equation 1:

The number of pounds of the 50 cents per pound nuts (x) plus the number of pounds of the 80 cents per pound nuts (y) equals 30 pounds.

x + y = 30

Equation 2:

The cost of the 50-cent-per-pound nuts (50x) + the cost of the 80-cent-per-pound nuts (80x) equals 75 cents per pound times 30 pounds, or 2250 cents ($22.50):

50x + 80y = 75(30) = 2250

To make things a little easier, you can divide both sides of this equation by 10:

5x + 8y = 225
x + y = 30

There are now lots of ways to solve. I like the addition method, so I'm going to multiply the bottom one by -5:

5x + 8y = 225
-5x - 5y = -150

Adding the two together, you get 3y = 75, so y = 25.

Then, since x + y = 30, x = 30 - y = 30 - 25 = 5.

So he'd use 5 pounds of 50-cents-per-pound nuts, and 25 pounds of 75-cents-per-pound nuts.

Answer 3

50x + 80y = 75(x+y) (using cents)

50x + 80y = 75x + 75y

5y = 25x
y = 5x (basically, you need a 5 to 1 ratio of expensive to cheap nuts)

We want x+y = 30 total.
x + 5x = 30
6x = 30
x = 5
y = 30 - 5 = 25

Checking the math: 5*.5 + 25*.8 = $22 which is $22.5/30 = $.75 per pound

Answer 4

Thirty pounds of nuts at 75 cents has to cost $22.50. Therefore, you need 25 pounds of the $.80 nut to equal $20. Last of all, you need 5 pounds of the $.50 nuts costing $2.50. Added together the nuts will cost $22.50

Answer 5

Jim is right, but to explain:

Let x = pounds of $0.50/lb. nuts
Let y = pounds of $0.80lb. nuts

The known part of the equation is the mix of 30lbs at $0.75/lb

So we have:

$0.50x + $0.80y = $22.50

One way to visualize this is by graphing. Make an x-y charrt:

x I y
45 0
0 28.125

See where these lines intercept for answer.