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!

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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