SOLUTION: how do i setup an equation for the following problem i am very confused: HOW MANY POUNDS OF NUTS WORTH $4.20 PER POUND MUST BE MIXED WITH 12 POUNDS OF NUTS WORTH $3 PER POUND TO P

Question 498653: how do i setup an equation for the following problem i am very confused: HOW MANY POUNDS OF NUTS WORTH $4.20 PER POUND MUST BE MIXED WITH 12 POUNDS OF NUTS WORTH $3 PER POUND TO PRODUCE A MIXTURE THAT CAN BE SOLD FOR $3.90 PER POUND
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Try this!
Let x = the required number pounds of the nuts worth $4.20 per pound.
We can express the cost of these x pounds of nuts as:
$4.20(x). Now we want to add this to 12 pounds of nuts worth $3.00 per pound the cost of which can be expressed as: $3.00(12).
Now if we add these together, we get:
$4.20(x)+$3.00(12) and this sum is to equal (12+x) pounds of nut mixture to cost $3.90 per pound. Now we can write the equation to solve for x.
4.20(x)+3.00(12) = (12+x)(3.90) Simplify.
4.2x+36 = 46.8+3.9x Subtract 3.9x from both sides.
0.3x+36 = 46.8 Now subtract 36 from both sides.
0.3x = 10.8 Finally, divide both sides by 0.3
x = 36
You will need to mix 36 pounds of nuts worth $4.20 per pound with 12 pounds of nuts worth $3.00 per pound to obtain 48 (12 + 36) pounds of nuts worth $3.90 per pound.
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