Solving Fraction Word Problems in Algebra

[Pseudo Statistic]

Hey,
I'm having some problems with some Fraction Word Problems in Algebra, can anyone assist me as to how I'm supposed to create my equations from the following two word problems in order to solve?
Thanks:

1) A 150mL solution of alcohol in water is 75% alcohol. How many mL of a 67% solution should be added to make the solution 72% alcohol? Let x - the number of mL of 67% solution to be added.

2) One pipe can fill a tank in 7 minutes less time than it takes a smaller pipe. Together they can fill the tank in 12 minutes. How long would it take the larger pipe to fill the tank? Let t = the number of minutes it takes the larger pipe to fill the tank alone.

For 2 I'm guessing it's t + (t - 7) = 12 ?

Thanks.

 

[teclo]

Hey,
I'm having some problems with some Fraction Word Problems in Algebra, can anyone assist me as to how I'm supposed to create my equations from the following two word problems in order to solve?
Thanks:

1) A 150mL solution of alcohol in water is 75% alcohol. How many mL of a 67% solution should be added to make the solution 72% alcohol? Let x - the number of mL of 67% solution to be added.

2) One pipe can fill a tank in 7 minutes less time than it takes a smaller pipe. Together they can fill the tank in 12 minutes. How long would it take the larger pipe to fill the tank? Let t = the number of minutes it takes the larger pipe to fill the tank alone.

For 2 I'm guessing it's t + (t - 7) = 12 ?

Thanks.

1. did you try to set this one up?

hint -- you are dealing with percent alchol times volume

2.

that method works, but look at what t is supposed to equal. is it what you've got it set equal to? should the time it takes the large pipe to fill up the tank be longer than the time it takes for the small pipe to fill up the tank?

what does t-7 symbolize? in that case what is the t in your equation?

hopefully those help

 

[Pseudo Statistic]

Oh, sorry, for t I meant t + 7 where t is the larger tank and t + 7 is the smaller..
Is this a proper equation set up?
For 1, I have absolutely NO CLUE how to set it up, our teacher explained it terribly and I have a test tomorrow on this. :-\
Hope you could explain 1 for me (Just the formation of the equation..) and tell me if 2 was correct!
Thanks alot.

 

[teclo]

Oh, sorry, for t I meant t + 7 where t is the larger tank and t + 7 is the smaller..
Is this a proper equation set up?
For 1, I have absolutely NO CLUE how to set it up, our teacher explained it terribly and I have a test tomorrow on this. :-\
Hope you could explain 1 for me (Just the formation of the equation..) and tell me if 2 was correct!
Thanks alot.

yes that is correct (numeber 2)

here's an idea for 1

amount of alcohol + amount of alcohol added = new % alcohol * total volume

how would you express the amount of alcohol knowing the solutions conentration and volume. you know the volume of one, your variable is the volume of the add. hopefully that helps?

 

[Pseudo Statistic]

0.75(150) + 0.67x = 0.72(150) ?
Sorry if I'm getting this wrong.
Hopefully you can tell me if I'm thinking the right way?
Thanks.

 

[teclo]

0.75(150) + 0.67x = 0.72(150) ?
Sorry if I'm getting this wrong.
Hopefully you can tell me if I'm thinking the right way?
Thanks.

look at your final volume -- is it 150 mL, or something else?

(hint: something else)

 

[Pseudo Statistic]

...
I wrote 0.72(150)...
You said:
amount of alcohol + amount of alcohol added = new % alcohol * total volume
And the amount of Alcohol originally is 0.75(150) and we're adding 0.67 or 67% of x to get 72% of 150, or 0.75(150)
Isn't that how you described it?!

 

[teclo]

...
I wrote 0.72(150)...
You said:
amount of alcohol + amount of alcohol added = new % alcohol * total volume
And the amount of Alcohol originally is 0.75(150) and we're adding 0.67 or 67% of x to get 72% of 150, or 0.75(150)
Isn't that how you described it?!

you're starting with 150 mL of the initial solution. when would the final volume equal the initial volume when you're adding something? (hint: only if you are adding 0 of the new solution).

so if you're diluting the initial sample, what way is your volume going to go? by how much?

 

[Pseudo Statistic]

I'm going to guess that you meant 0.75(150) + 0.67(x) = 0.72(0.75(150))
Yes, I know, I am a hopeless case. :(

 

[teclo]

I'm going to guess that you meant 0.75(150) + 0.67(x) = 0.72(0.75(150))
Yes, I know, I am a hopeless case. :(

look at what your right hand is saying. 72 % of 75 % of 150 mL

does that make sense?

your final conentration of solution is to be 72 %
your final volume is going to be the initial volume plus some amount of additional solution.
what is your variable representing?

in that case, what is your final volume?

 

[Pseudo Statistic]

Ahhhhhhhhhhh...
Sorry, I finally get it.. (I need some sleep, and I hope I got it!)
0.75(150) + 0.67(x) = 0.72(150 + x)
This better be right. :-\

 

[teclo]

looks good to me, test it out and see if the answer works and makes sense.

 

[Pseudo Statistic]

x = 90
That makes sense to me..
It's 2AM and I need sleep, have a nice day! ;)