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Two tailors, Janet and Samantha, sit down to do some embroidery. Janet can embroider 2 shirts per hour, and Samantha can get through 3 shirts per hour. In addition, the tailors had previously finished some shirts. Janet has already completed 15 shirts, and Samantha has completed 10 shirts. Janet and Samantha decide to take a break when they have finished the same total number of shirts. How many shirts, in total, will each tailor have finished?
Write a system of equations, graph them, and type the solution.

Two tailors, Janet and Samantha, sit down to do some embroidery. Janet can embroider $2$ shirts per hour, and Samantha can get through $3$ shirts per hour. In addition, the tailors had previously finished some shirts. Janet has already completed $15$ shirts, and Samantha has completed $10$ shirts. Janet and Samantha decide to take a break when they have finished the same total number of shirts. How many shirts, in total, will each tailor have finished? $\newline$ Write a system of equations, graph them, and type the solution.

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Mean, variance, and standard deviation of binomial distributions

Full solution

Q. Two tailors, Janet and Samantha, sit down to do some embroidery. Janet can embroider

2

shirts per hour, and Samantha can get through

3

shirts per hour. In addition, the tailors had previously finished some shirts. Janet has already completed

15

shirts, and Samantha has completed

10

shirts. Janet and Samantha decide to take a break when they have finished the same total number of shirts. How many shirts, in total, will each tailor have finished?

\newline

Write a system of equations, graph them, and type the solution.

Janet's rate and progress: Janet's rate is $2$ shirts per hour, and she has already completed $15$ shirts.
Samantha's rate and progress: Samantha's rate is $3$ shirts per hour, and she has already completed $10$ shirts.
Representation of hours worked: Let $x$ represent the number of hours they both work before taking a break.
Total shirts completed by Janet: The total number of shirts Janet will have finished is $15 + 2x$ .
Total shirts completed by Samantha: The total number of shirts Samantha will have finished is $10 + 3x$ .
Setting up equation for equal total shirts: They take a break when they have finished the same total number of shirts, so we set the two expressions equal to each other: $15 + 2x = 10 + 3x$ .
Solving for x: Subtract $2x$ from both sides to get: $15 = 10 + x$ .

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