Median AM and CN of △ABC intersect at point O. What part of area of △ABC is the area of △AON?
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Answer:
10 pounds of raisins and 10 pounds of peanuts.
Step-by-step explanation:
Let c represent the pounds of chocolate covered raisins.
Let p represent the pounds of peanuts.
We know that the raisins cost $1.50 per pound and the peanuts cost $1.20 per pound.
Ameenah wants to make 20 pounds of a mixture of the raisins and peanuts that sells for 1.35 a pound. So, we can write the following expression:
This represents the cost given c pounds of raisins and p pounds of peanuts.
Ameenah wants to combine c and p to make them 1.35 per pound. In other words, the expression must equal:
We also know that she wants to make 20 pounds. So, c plus p must total 20. Therefore:
We now have the system of equations:
First, since we know that c+p is 20, we can substitute that into the first equation.
Second, let's subtract p from both side for the second equation to isolate a variable. So:
Let's now substitute this into the first equation:
Distribute:
Combine like terms:
Subtract 30 from both sides:
Divide both sides by -0.3. So, the amount of peanuts needed is:
10 pounds of peanuts is needed.
This means that 20-10 or 10 pounds of raisins is needed.