Staples recently charged $17.99 per box of Pilot Precise rollerball pens and $7.49 per box for Bic Matic Grip mechanical pencils. If Kelling Community College purchased 120 such boxes for a total of $1234.80, how many boxes of each type did they purchase?
Let x = boxes of Pilot and y = boxes of Bic
x + y =120 therefore
x = 120 - y
17.99x + 7.49y = 1234.8
Substitute 120-y for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
32 boxes of pilot and 88 boxes of Bic
32x17.99 = 575.68
88x 7.49 = 659.12
total = 1234.80
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To solve this problem, we can use a system of equations. Let's assign variables to the unknowns:
Let x represent the number of boxes of Pilot Precise rollerball pens.
Let y represent the number of boxes of Bic Matic Grip mechanical pencils.
From the given information, we can set up two equations:
1. The total cost equation:
17.99x + 7.49y = 1234.80
2. The total number of boxes equation:
x + y = 120
Now, we have a system of equations to solve simultaneously.
To start, let's isolate x in equation 2:
x = 120 - y
Substituting this value of x into equation 1, we get:
17.99(120 - y) + 7.49y = 1234.80
Now, we can solve this equation for y:
2158.80 - 17.99y + 7.49y = 1234.80
2158.80 - 10.50y = 1234.80
-10.50y = 1234.80 - 2158.80
-10.50y = -924.00
y = -924.00 / -10.50
y = 88
Now, we can substitute the value of y back into equation 2 to solve for x:
x + 88 = 120
x = 120 - 88
x = 32
Therefore, Kelling Community College purchased 32 boxes of Pilot Precise rollerball pens and 88 boxes of Bic Matic Grip mechanical pencils.