Rachael bought 12 pencils and 7 markers for $5.36, and later bought 8 pencils and 5 markers for $3.68. Find the cost of each pencil and marker.
Let x = cost of pencils and y = cost of markers.
12x + 7y = 5.36
8x + 5y = 3.68
Multiply second equation by 1.5.
12x + 7.5y = 5.52
Subtract first equation from modified second equation.
.5y = .16
y = .32
Insert value of y into either equation to find x. Then put both values in the other equation to check your answers.
To find the cost of each pencil and marker, we can set up a system of equations based on the given information.
Let's say the cost of each pencil is 'p' dollars and the cost of each marker is 'm' dollars.
From the first purchase:
12p + 7m = 5.36 ---(Equation 1)
From the second purchase:
8p + 5m = 3.68 ---(Equation 2)
Now, we have a system of two equations with two variables. We can solve this system to determine the cost of each pencil and marker.
First, let's eliminate one of the variables. We'll multiply Equation 2 by 7 and Equation 1 by 5 to make the coefficients of 'm' the same in both equations:
35m + 56p = 25.76 ---(Equation 3)
35m + 49p = 37.44 ---(Equation 4)
Now, we can subtract Equation 4 from Equation 3 to eliminate 'm':
35m - 35m + 56p - 49p = 25.76 - 37.44
7p = -11.68
Divide both sides of the equation by 7 to solve for 'p':
p = -11.68 / 7
p ≈ -1.668
Since the cost of an item cannot be negative, we made a mistake or encountered inconsistent information. Please double-check the provided values and the equations given.