Leah and Christopher work at a dry cleaners ironing shirts. Leah can iron 25 shirts per hour, and Christopher can iron 15 shirts per hour. Leah and Christopher worked a combined 13 hours and ironed 265 shirts. Write a system of equations that could be used to determine the number of hours Leah worked and the number of hours Christopher worked. Define the variables that you use to write the system.

25x + 15y = 265

x+y = 13

Step-by-step explanation:

Step 1:

Given

Number of shirts Leah can iron in an hour = 25 shirts

Number of shirts Christopher can iron in an hour = 15 shirts

Total number of hours worked by both = 13 hours

Total number of shirts ironed by them = 265 shirts

Step 2 :

Let x represent the number of hours Leah works and y represent the number of hours Christopher works

Leah irons 25 shirts in one hour, so in x hours he would iron 25x shirts

Christopher irons 15 shirts in one hour, so in y hours he would iron 15y shirts

Given total shirts ironed by them together is 265 , we have

25x + 15y = 265

They worked a combined of 13 hours, so

x+y = 13

Step 3:

The system of equations that could be used to determine the number of hours Leah worked and the number of hours Christopher worked are ,

25x + 15y = 265

x+y = 13

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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step-by-step explanation: