Paint Town sold 45 paintbrushes, one
kind at $8.50 each and another at $9.75 each. In all,
$398.75 was taken in for the brushes. How many of
each kind were sold?
x and 45-x
x(8.50) + (45-x)(9.75) = 398.75
try it from there
To solve this problem, let's assign variables to represent the number of each kind of paintbrush sold.
Let's call the number of paintbrushes sold at $8.50 each "x" and the number of paintbrushes sold at $9.75 each "y".
We know that Paint Town sold a total of 45 paintbrushes, so we can write the equation:
x + y = 45 -- Equation 1
We also know that the total amount of money taken in for the brushes was $398.75. Since each paintbrush sold at $8.50 and each paintbrush sold at $9.75, we can write the equation:
8.50x + 9.75y = 398.75 -- Equation 2
Now we have a system of equations with two equations and two unknowns.
To solve the system, we can use substitution or elimination method. Let's use the elimination method.
Let's multiply Equation 1 by -8.50 to eliminate the x term:
-8.50(x + y) = -8.50(45)
-8.50x - 8.50y = -382.50 -- Equation 3
Now, we can add Equation 3 to Equation 2:
(-8.50x - 8.50y) + (8.50x + 9.75y) = -382.50 + 398.75
-8.50x + 8.50x - 8.50y + 9.75y = 16.25
1.25y = 16.25
Simplifying this equation, we find:
y = 16.25 / 1.25
y = 13
Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:
x + 13 = 45
x = 45 - 13
x = 32
Therefore, Paint Town sold 32 paintbrushes at $8.50 each and 13 paintbrushes at $9.75 each.