story problem? help for the whole thing

[alltimelowlove]

I need help figuring out this entire problem, I do not understand it at all.
I don't even really know how to start it.
My teacher said to make a table to solve it, but I'm not sure how.

"A potter is making cups and plates. It takes her 6 minutes to make a cup and 3 minutes to make a plate. Each cup uses 3/4 lb. of clay and each plate uses 1 lb. of clay. She has 20 hours available for making the cups and plates and has 250 lbs. of clay on hand. She makes a profit of $2.00 on each cup and $1.50 on each plate. How many cups and plates should she make in order to maximize her profit?"

I really need help on this and a thorough explanation of how to do it.

 

[NovaDragon]

You would first set up constraints for the story problem.

Cup=x

Plate=y
--------------------------
6x+3y?1200 (1200 minutes in 20 hours)

.75x+y?250
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Now just solve it like a system of equation problem.
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Set up the problem for elimination
3(.75x+y)=3(250)

2.25x+3y=750
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Now subtract

(6x+3y=1200)-(2.25x+3y=750)=3.75x=450
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Now solve for x

450/3.75=120

x=120
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plug x back into an equation and solve for y

6(120)+3y=1200

720+3y=1200

1200-720=480

3y=480

y=160
-----------------------------------------
x=120, y=160

120 cups, 160 plates

 

[Deleted member 4993]

I need help figuring out this entire problem, I do not understand it at all.
I don't even really know how to start it.
My teacher said to make a table to solve it, but I'm not sure how.

"A potter is making cups and plates. It takes her 6 minutes to make a cup and 3 minutes to make a plate. Each cup uses 3/4 lb. of clay and each plate uses 1 lb. of clay. She has 20 hours available for making the cups and plates and has 250 lbs. of clay on hand. She makes a profit of $2.00 on each cup and $1.50 on each plate. How many cups and plates should she make in order to maximize her profit?"

I really need help on this and a thorough explanation of how to do it.

Let

the # of cups = C

the # of plates = P

It takes her 6 minutes to make a cup and 3 minutes to make a plate. She has 20 hours available for making the cups and plates ? 0.1* C + 0.05*P ? 20

Each cup uses 3/4 lb. of clay and each plate uses 1 lb. of clay. She ...has 250 lbs. of clay on hand. ? C * 0.75 + P * 1.0 ? 250

Now continue.....