writing equations

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Fteacher90

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May 27, 2019
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It takes each worker 1hr to make jeans, and 1 ½ hours to make a pair of shoes.
They will only work a total of 16 hours a day (meaning 8 hours each) and that they will only make 20 items per day.
how to build an equation with this and graph it?

I was going to use T/A + T/B =1
where T=time working together, A=the time for person A working alone, B=the time for person B working alone
then i just got lost

please help
 
Hello, and welcome to FMH! :)

This isn't a question of finding how long it takes two entities to complete a task working together, given their individual rates. since both workers work at the same rate, and for the same length of time, I would simply focus on one worker. Let \(J\) be the number of jeans produced in 8 hours and \(S\) be the number of pairs of shoes produced.

We may then write:

[MATH]J+\frac{3}{2}S=8\implies 2J+3S=16[/MATH]
[MATH]J+S=20[/MATH]
What do you get when you solve this system?
 
mmm4444bot, i apologize, this is my first post. i did not find this exercise in a book, it was on a test from school. I changed some stuff around so that it was not the same question as the test.

Thank you MarkFL!

SO....then i would substitute the letters with the number of hours it takes for each task to be completed ?
2(1)+3(1.5)=6.5 ?
or did i butcher that completely ?
 
I would use elimination to solve the system. You're going to find that in changing things around, you've made the problem produce nonsensical results. That was why I asked you what you get.

I would write the first equation as I gave it, and multiply the second equation by -2 so that I have:

[MATH]2J+3S=16[/MATH]
[MATH]-2J-2S=-40[/MATH]
Now, we can add the equations together to eliminate \(J\)...and we get:

[MATH]S=-24[/MATH]
This is where we realize something isn't right. :)
 
i think its confusing me more that it's negative because how can they make negative 24 shirts ? wouldnt we be able to make the equation so that when you plug in the answer, the problem will then solve for jeans ?
 
Fteacher90 said:
i think its confusing me more that it's negative because how can they make negative 24 shirts ? wouldnt we be able to make the equation so that when you plug in the answer, the problem will then solve for jeans ?
Click to expand...

Yes, you could then use that value for \(S\) in either of the 2 original equations to find \(J\), which would be 44. This is the algebraic solution, but as we can see the result doesn't make sense. Care must be taken when changing a problem to make sure it continues to have a solution that makes sense.
 
Yes, so the original question asks to create an equation using the information above, and then be able to graph the results using that equation.
im assuming that this would work similar to other linear equations.

so i would use 2J + 3S = 16 and
subtract 2J from both sides
leaving me with
3S = 16-2J

divide both sides by 3 leaving me with

S= 5 3/10 - 2/3J

? is that right

I just replaced x's and y's with j's and s's in this problem. The problem itself is almost identical to the test question that was given. the only part i changed about the question was what was being made by the workers. If the problem doesnt make sense, its my teachers fault o_O
 
MarkFL said:
Yes, you could then use that value for \(S\) in either of the 2 original equations to find \(J\), which would be 44. This is the algebraic solution, but as we can see the result doesn't make sense. Care must be taken when changing a problem to make sure it continues to have a solution that makes sense.
Click to expand...
i just plugged your answer and i got 44 as well. Thank you for your patience as i try to understand.
 
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