Question

How many pounds of walnuts that cost $0.80 per pound must be mixed

with 8 pounds of cashews that costs $1.25 per pound to make a mixture of
nuts that costs $1.00 per pound?

Answer 1

You would need to mix in 10 lbs of Walnuts in order for it to equal $1.00 per pound. We started off with 8 lbs of Cashews at $1.25 per lb, which is $10. Since walnuts cost $0.80 per lb, it would be $8.00 for 10 lbs of Walnuts, which would be in total 18 lbs for $18.00. To find the cost per lb we divide the weight by the total price, 18 lbs / $18.00 makes it a $1.00 per lb.

Answer 2

The number of walnut pounds we need to add is 10

Explanation:

We need to make a mixture that costs $1 per pound.

That means that the total cost of our mixture, divided by the number of pounds must be equal to 1.

`(MixtureCost)/(NumberOfPounds) = 1`

Well, we know that the total cost of our mixture is equal to the cost of the cashews + cost of walnuts.

`MixtureCost = CashewsCost + WalnutsCost`

We also know that we'll buy 8 pounds of cashews that cost $1.25 each and some amount of pounds (which we'll call x) of walnuts that cost $0.80.

Knowing all of that, we can write this:

`MixtureCost=8*1.25 + x*0.8`

If we make that multiplication, we have that

`MixtureCost=10+x*0.8`

Now that we know the cost of our mixture, we just need to know the total number of pounds... But we already know that, don't we?

We know that there are 8 pounds of cashews and x pounds of walnuts, so here's what we can write:

`NumberOfPounds=8+x`

Now, if we plug in the values we found in the first equation, here's what we have:

`(10+x*0.8)/(8+x)=1`

The 8+x is dividing, so i'll pass it to the other side multiplying:

`10+0.8*x=x+8`

The 10 in the left side will go to the right side with a negative sign:

`0.8x=x-2`

Now, if I pass the x from the right side to the left one changing signs:

`0.8x-x=-2\\\\-0.2x=-2`

By changing signs from both sides, we have that:

`0.2x = 2\\\\x = 10`

Therefore, the number of walnut pounds we need to add is 10