Two coworkers picked up some writing instruments at the office supply store. Christina selected 6 boxes of pencils and 5 boxes of ballpoint pens, paying $21. Next, Rachel spent $30 on 3 boxes of pencils and 9 boxes of ballpoint pens. How much does a box of each cost?
Let x be the price of a box of pencils.
3x + 9y = 30
Note: y is the price of a box of ballpoint pens because we don't know the price.
Let x be the price of a box of pencils.
6x + 5y = 21
Multiply both sides of the first equation by 6 to make the coefficient of x equal to 6x.
18x + 54y = 180
Multiply both sides of the second equation by 3 to make the coefficient of x equal to 6x.
18x + 15y = 63
Subtract the second equation from the first equation to eliminate x.
39y = 117
The price of a box of ballpoint pens is y = 117 / 39 = <<117/39=3>>3.
Substituting the value of y into the equation 6x + 5y = 21, we get 6x + 5 * 3 = 21
Subtract 15 from both sides of the equation to get 6x = 21 - 15 = 6.
Divide both sides of the equation by 6 to get x = 6 / 6 = <<6/6=1>>1.
A box of pencils cost 1 dollar and a box of ballpoint pens cost 3 dollars. Answer: \boxed{1, 3}.