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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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) About Me  (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 x%2By=10.


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 9x%2B6.5y=8%2810%29. Multiply 8 and 10 to get 80. So the equation then becomes 9x%2B6.5y=80. Finally, multiply EVERY term by 10 to make every number a whole number. So the equation then becomes 90x%2B65y=800



So we have the system of equations:

system%28x%2By=10%2C90x%2B65y=800%29


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

x%2By=10 Start with the first equation


y=10-x Subtract x from both sides


y=-x%2B10 Rearrange the equation


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

Since y=-x%2B10, we can now replace each y in the second equation with -x%2B10 to solve for x



90x%2B65highlight%28%28-x%2B10%29%29=800 Plug in y=-x%2B10 into the second equation. In other words, replace each y with -x%2B10. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



90x%2B%2865%29%28-1%29x%2B%2865%29%2810%29=800 Distribute 65 to -x%2B10


90x-65x%2B650=800 Multiply


25x%2B650=800 Combine like terms on the left side


25x=800-650Subtract 650 from both sides


25x=150 Combine like terms on the right side


x=%28150%29%2F%2825%29 Divide both sides by 25 to isolate x



x=6 Divide





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


So the first part of our answer is: x=6









Since we know that x=6 we can plug it into the equation y=-x%2B10 (remember we previously solved for y in the first equation).



y=-x%2B10 Start with the equation where y was previously isolated.


y=-%286%29%2B10 Plug in x=6


y=-6%2B10 Multiply


y=4 Combine like terms



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


So the second part of our answer is: y=4









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

So our answers are:

x=6 and y=4


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