System of Equations Word Problems

by Katie
(New Jersey)

I really NEED help with these System of Equations word problems! I did the ones on this website but I want an example that can help with mixes of trail mixes or snacks. Please help me!


Karin From Algebra Class Says:


Katie,

Systems of Equations is a tough unit for many students. I would love to help you with the problem that you are having difficulty with, but I need you to give me an example!

Comment on this thread, with the systems of equations word problem that you need help with and I will be glad to help!

Thanks,
Karin

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Jan 20, 2012
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by: Lydthakid

Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold?

Karin From Algebra Class Says:



This is an interesting problem involving the pitchers!

Let x = number of cups the small pitcher holds
Let y = number of cups the large pitcher holds

Now, we must use the information to write 2 equations.

2 small + 1 large = 8 cups
2x + y = 8

1 large - 1 small = 2 cups
y - x = 2

Now that we have two equations, we can solve.
I will use the substitution method to solve.
First I will second equation for y so that I can substitute it into the second equation.

y - x + x = 2 + x
y = x+2

Now, we'll substitute this into the first equation.

2x+y = 8
2x + x+2 = 8

Combine like terms:
3x+2 = 8

Solve for x:
3x+2-2 = 8-2
3x = 6
3x/3 = 6/3
x = 2

Since x = 2, this means that the small pitcher holds 2 cups.

Let's substitute 2 for x into the second equation to find y.

y -x = 2
y - 2 = 2

Now solve for y:
y-2+2 = 2+2
y = 4

Since y = 4, we know the large pitcher holds 4 cups.

The small pitcher holds 2 cups and the large pitcher holds 4 cups.

Hope this helps!
Karin

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