this a system of equations
A merchant decides to mix peanuts worth 5.25 per pound and trail mix worth 2.75 a pound to make a 10 pound mixture worth 4.75 per pound. how many pounds of each should his mixture contain?
please help me.
If there are p lbs of peanuts, then the rest (10-p) lbs of trail mix.
Now just add up the value of each part to equal the value of the final mixture:
5.25p + 2.75(10-p) = 4.75*10
To solve this problem, we can set up a system of two equations using the given information.
Let's assume the merchant uses x pounds of peanuts and (10 - x) pounds of trail mix.
The value equation can be written as:
(5.25)(x) + (2.75)(10 - x) = (4.75)(10)
Now we can simplify and solve for x.
Multiply the values:
5.25x + 2.75(10 - x) = 4.75(10)
Expand the parentheses:
5.25x + 27.5 - 2.75x = 47.5
Combine like terms:
2.5x + 27.5 = 47.5
Subtract 27.5 from both sides:
2.5x = 20
Now, divide both sides by 2.5:
x = 8
Therefore, the merchant should use 8 pounds of peanuts and 2 pounds of trail mix to make the desired mixture.