Algebra Word Problems

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January 30th 2009, 10:42 AM
kanej316

Algebra Word Problems

I have 2 word problems in which I need to set up the equation and arrive at an answer. I am not exactly asking for an answer to these problems, I just need help in setting the labels and equations up. For question one I have most of the information, but not for question two. The areas typed in red are the areas that I need help with. THANK YOU SOOOO MUCH!!!

1) A chemist needs 140 mL of a 32% solution but has only 22% and 50% solutions available. Find how many mL of each that should be mixed to get the desired solution.
*(Verbal Model): #of mL of 22% solution + # of mL of 50% solution=140mL of 32% solution
*(Labels): #of mL of 22% solution=x, #of mL of 50% solution=140-x, amount of 22% solution=0.22x, amount of 50% solution= .50(???), amount of 32% solution= .32(???)
*(Equation): .22x + .50(???) = .32(???)

2) Two pumps can fill a water tank in 45 minutes when working together. Alone the second pump takes 3 times longer than the first to fill up the tank. How long does it take the first pump alone to fill the tank?
*(Verbal Model):
*(Labels):
*(Equation):
January 30th 2009, 11:01 AM
earboth

Quote:

Originally Posted by kanej316

...

1) A chemist needs 140 mL of a 32% solution but has only 22% and 50% solutions available. Find how many mL of each that should be mixed to get the desired solution.
*(Verbal Model): #of mL of 22% solution + # of mL of 50% solution=140mL of 32% solution
*(Labels): #of mL of 22% solution=x, #of mL of 50% solution=140-x, amount of 22% solution=0.22x, amount of 50% solution= .50(???), amount of 32% solution= .32(???)
*(Equation): .22x + .50(???) = .32(???)

...

You only have to do one step and use all the terms you've found by yourself:

$0.22 \cdot x + 0.50 \cdot (140-x) = 0.32 \cdot 140$

Expand the bracket and solve for x. (For confirmation only: x = 90)
January 30th 2009, 11:11 AM
earboth

Quote:

Originally Posted by kanej316

...
2) Two pumps can fill a water tank in 45 minutes when working together. Alone the second pump takes 3 times longer than the first to fill up the tank. How long does it take the first pump alone to fill the tank?
*(Verbal Model):
*(Labels):
*(Equation):

Let T denote the volume of the tank and x the number of minutes, it takes the first pump to fill the tank.

Then the second pump will need 3x minutes to fill the tank.

$\dfrac Tx$ is the amount of water which comes from the first pump in one minute;

$\dfrac T{3x}$ is the amount of water which comes from the second pump in one minute.

Together they are working during 45 minutes and then the tank is filled:

$\left(\dfrac Tx + \dfrac T{3x} \right) \cdot 45\ min = T$

Expand the bracket and solve for x. (For confirmation only: x = 60)