A box of chalk and 2 staplers cost $10. Three boxes of chalk and 2 staplers cost $18. Find the total cost of 1 box of chalk and 1 stapler.
staples = s
chalk = c
c + 2s = 10
3c + 2s = 18
-c-2s = -10
3c + 2s = 18
2c = 8
c = 4
s = 3
c + s
4 + 3 = 7
The total cost $7.
To solve this problem, we can use a system of equations. Let's assign variables to the unknowns: let's say the cost of one box of chalk is "x" dollars and the cost of one stapler is "y" dollars.
From the given information, we can form the following equations:
Equation 1: x + 2y = 10 (One box of chalk and 2 staplers cost $10)
Equation 2: 3x + 2y = 18 (Three boxes of chalk and 2 staplers cost $18)
We can solve this system of equations using substitution or elimination. Let's use elimination to solve for x and y:
Multiply Equation 1 by 3 and Equation 2 by 1 to make the coefficients of "y" the same:
3(x + 2y) = 3(10) (Equation 1 multiplied by 3)
1(3x + 2y) = 1(18) (Equation 2 multiplied by 1)
Now we have:
3x + 6y = 30
3x + 2y = 18
Subtract the second equation from the first to eliminate x:
(3x + 6y) - (3x + 2y) = 30 - 18
4y = 12
Divide both sides of the equation by 4:
y = 3
Now substitute the value of y back into Equation 1:
x + 2(3) = 10
x + 6 = 10
Subtract 6 from both sides of the equation:
x = 4
So, the cost of one box of chalk is $4 and the cost of one stapler is $3. The total cost of one box of chalk and one stapler is $4 + $3 = $7.