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Not including tax, a total of 19 pens and markers cost $11.50. The pens cost $0.25 each, and the markers cost $0.75 each. Write the system of equations that could be used to solve for the number of pens, p, and the number of markers, m, bought. (4 points) p+m = ! ip + :: 30.5 :: 0.75 m = 1 : 0.25 :: 1.50 1 :: 11.50 19
p + m = 19
0.25p + 0.75m = 11.50
To solve for the number of pens, p, and the number of markers, m, bought, we can set up the following system of equations:
Equation 1: p + m = 19
This equation represents the total number of pens and markers bought, which is 19 in this case.
Equation 2: 0.25p + 0.75m = 11.50
This equation represents the cost of the pens and markers, which is $11.50 in this case. Taking into consideration the individual costs of pens ($0.25 each) and markers ($0.75 each), we can multiply the number of pens by their cost and the number of markers by their cost, and then sum up these costs to get the total cost.
By solving this system of equations, we can determine the values of p and m, which represent the number of pens and markers bought, respectively.
To write a system of equations based on the given information, we can consider the following:
Let p be the number of pens bought.
Let m be the number of markers bought.
1. The total number of items bought is 19, given by p + m = 19.
2. The total cost of the pens and markers is $11.50. Since each pen costs $0.25 and each marker costs $0.75, we can calculate the total cost equation as:
(0.25 * p) + (0.75 * m) = 11.50.
Therefore, the system of equations is:
p + m = 19
0.25p + 0.75m = 11.50.
By solving this system of equations, we can find the values of p and m, which represent the number of pens and markers purchased, respectively.