1. ## Help on problems.

I'm not sure about solving problems, #1 and #2.
There seems to be different ways to answering these types of problems and the information/question they give varies form problem to problem. Is there a universal setup for these types of problems?

#1
A biologist wishes to have 15 gallons of an 80% formaldehyde solution. In her inventory, she has pure formaldehyde and some 50% formaldehyde solution. How many gallons of each should she mix to obtain the desired solution?

So do I set up the equation 2x+.50(15-x)=15(.80)
so x=3 gallons? ,15-3= 12 gallons

#2
A leather finisher determines that his 8-ounce solution of 12% boric acid is too weak. How many ounces of pure boric acid must be added to increase the concentration to 20%

15*(.12)which would equal: .96+x. Does that express what is needed to increase the boric acid and where does the 20% come in to play?

2. Originally Posted by Ash
I'm not sure about solving problems, #1 and #2.
There seems to be different ways to answering these types of problems and the information/question they give varies form problem to problem. Is there a universal setup for these types of problems?

#1
A biologist wishes to have 15 gallons of an 80% formaldehyde solution. In her inventory, she has pure formaldehyde and some 50% formaldehyde solution. How many gallons of each should she mix to obtain the desired solution?

So do I set up the equation 2x+.50(15-x)=15(.80)
so x=3 gallons? ,15-3= 12 gallons
I think you will find it easier to follow what is going on if you include more
text saying what you are doing.

Let x be the number of gallons of 100% solution, and y be the number of
gallons of 50% solution of formaldehyde used. Then as there are 15 gallons
altogether:

x + y =15.

Also the 15 gallons contains 0.8*15 gallons of pure formaldehyde, while
x gallons of the 100% solutions contain x gallons or pure formaldehyde, and
y gallons of 50% solution contain 0.5*y or pure formaldehyde, so:

0.8*15 = x + 0.5*y,

or rearranging:

x + 0.5 y = 12

so now we have two equations:

x + y = 15
x + 0.5y =12

which we solve to find that y=6 gallons and x = 9 gallons.

RonL

3. Originally Posted by Ash
#2
A leather finisher determines that his 8-ounce solution of 12% boric acid is too weak. How many ounces of pure boric acid must be added to increase the concentration to 20%

15*(.12)which would equal: .96+x. Does that express what is needed to increase the boric acid and where does the 20% come in to play?
Let the number of onces of pure boric acid added be x, then we have 8+x
ounces of solution, which contains 0.12*8 + x ounces of pure boric acid.

So as the final concentration is 20%:

(0.12*8 + x)/(8 + x) = 0.2

or:

0.96 + x = 1.6 + 0.2 x

so:

0.8 x = 1.6 - 0.96,

so: x = 1.05 ounces.

RonL

4. Originally Posted by CaptainBlack
I think you will find it easier to follow what is going on if you include more
text saying what you are doing.

RonL

Thanks for your help! Next time I will include more text so that the part I am not doing right or understanding can be easier identified.