box of chalk and 2 staplers cost $10.00. Three boxes of chalk and 2 staplers cost $18.00. How much is a box of chalk and a stapler?
x is box of chalk
y is staplers
x + 2y = 10
3x + 2y = 18
solve for x and then plug in and solve for y
x+2y=10
3x+2y=18
Multiply the first equation by -1 to cancel the y's:
-x-2y=-10
3x+2y=18
Now add the rows
2x=8
x=?
Now plug that back into either original equation to solve for y.
16
the answer is
To solve this problem, we need to set up a system of equations. Let's assume the cost of a box of chalk is "C" dollars and the cost of a stapler is "S" dollars.
From the given information, we can write two equations:
First equation: C + 2S = 10.00 (equation 1) - This represents the cost of one box of chalk and two staplers, which totals $10.00.
Second equation: 3C + 2S = 18.00 (equation 2) - This represents the cost of three boxes of chalk and two staplers, which totals $18.00.
Now, we can solve this system of equations using either substitution or elimination method. Let's use the elimination method to solve it.
Multiply equation 1 by 3:
3C + 6S = 30.00
Now, subtract equation 2 from the modified equation:
(3C + 6S) - (3C + 2S) = (30.00 - 18.00)
After simplifying, we have:
4S = 12.00
Divide both sides of the equation by 4:
S = 3.00
Now, substitute the value of S (3.00) into equation 1:
C + 2(3.00) = 10.00
Simplifying, we get:
C + 6.00 = 10.00
Subtract 6.00 from both sides:
C = 4.00
Therefore, a box of chalk and a stapler cost $4.00.