SOLUTION: Nuts costing $9 per kg are to be mixed with nuts costing $6.5 per kg to make 10 kg of nuts costing $8 per kg. How many kg of nuts costing $9 per kg should be used? Please help me!

Question 189685: Nuts costing $9 per kg are to be mixed with nuts costing $6.5 per kg to make 10 kg of nuts costing $8 per kg. How many kg of nuts costing $9 per kg should be used?
Please help me!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let
x = amount of $9 nuts
y = amount of $6.5 nuts

Since we "to make 10 kg of nuts", this gives the first equation .

Also, since "$9 per kg are to be mixed with nuts costing $6.5 per kg to make 10 kg of nuts costing $8 per kg.", this means that . Multiply 8 and 10 to get 80. So the equation then becomes . Finally, multiply EVERY term by 10 to make every number a whole number. So the equation then becomes

So we have the system of equations:

Let's solve by substitution

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 650 from both sides

Combine like terms on the right side

Divide both sides by 25 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

This means that 6 kg of $9 nuts and 4 kg of $6.50 nuts are needed
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