My brain hit the brakes

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smcelhaney

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How much water do I need to add to an existing 3800 gallons of a tank mix with a chemical at an 8 oz/100 gallon ratio to make it a 6 oz/100 gallon mix?
 
smcelhaney said:
How much water do I need to add to an existing 3800 gallons of a tank mix with a chemical at an 8 oz/100 gallon ratio to make it a 6 oz/100 gallon mix?
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1st you need to figure out how many oz of the chemical is in 3800 gallons knowing that every 100 gallons have 8oz of the chemical in it.

Suppose there are y oz of chemicals in the 3800 gal mixture and then we add x gallons of water.

Then y/(3800+x) = 6/100. Now solve for x
 
smcelhaney said:
How much water do I need to add to an existing 3800 gallons of a tank mix with a chemical at an 8 oz/100 gallon ratio to make it a 6 oz/100 gallon mix?
Click to expand...
You have 3800 gallons = 38(100) gallons of 8-oz-in-100-gal ratio. So how many hundred-gallon sets do you have? (Hint: Divide.) So how many six-ounce sets do you have? (Hint: It's the same number.) So how many ounces do you have? (Hint: Multiply.)

You need a mix that is 6-oz-in-100-gal ratio. Since you want a mixture which is more dilute (that is, which has less chemical per hundred gallons of water), you'll be adding more water.

Given the number of ounces you have, how many six-ounce sets is this? (Hint: Divide. Leave the result in exact fractional form.) Given the number of six-ounce sets you need, how many 100-gallon sets do you need, in total? (Hint: It's the same number.) Then how many gallons do you need, in total? (Hint: Multiply by 100.)

You know how many gallons you'd started with. So how many more gallons do you need? (Hint: Subtract.) ;)
 
All of my work is wrong. This is a real life situation for work. My boss came up with 1200, my mom and I talking through it (and her on the calculator) came up with 1266 and my dad came up with 1250. It hurts my brain so much. Years ago I would have solved this problem in way less time (and enjoyed doing it). It's so frustrating that my mind can't seem to wrap around this.:confused:

For some reason, I keep feeling like we didn't account for the fact that we were using 2 different measurements in our calculations and I'm afraid we will add the wrong amount.
 
smcelhaney said:
All of my work is wrong. This is a real life situation for work. My boss came up with 1200, my mom and I talking through it (and her on the calculator) came up with 1266 and my dad came up with 1250. It hurts my brain so much. Years ago I would have solved this problem in way less time (and enjoyed doing it). It's so frustrating that my mind can't seem to wrap around this.:confused:

For some reason, I keep feeling like we didn't account for the fact that we were using 2 different measurements in our calculations and I'm afraid we will add the wrong amount.
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let x be the amount of water (in gallons) that you need to add to the 3800 gallons of water.

You want this diluted mixture to have 6% of the chemical.

You can check any answer by computing the following and see if you get 6% or .06-->divide the number of ounces of chemical in the mixture (this amount did not change just because you added water!) by the total number of gallons which is (3800 + x).

(One of your answers will work)
 
smcelhaney said:
How much water do I need to add to an existing 3800 gallons of a tank mix with a chemical at an 8 oz/100 gallon ratio to make it a 6 oz/100 gallon mix?
Click to expand...

Really just repeating what has already been said with a slight addition. It is very helpful sometimes to keep the units with the problem in order to solve the problem. For example, how many oz O do you have
O = \(\displaystyle 3800 gal \frac{8 oz}{100 gal} \)
For units, the gal's cancel and you are left with oz. For the numbers you are left with 8 * 38. So
O = 304 oz.
Since the units came out right, you feel a little more comfortable about the answer.

Now you want a bunch of water ( x gal) with a concentration of 6 oz/gal and you have 304 oz. So
\(\displaystyle x gal \frac{6 oz}{100 gal} = 304 oz. \)
The gal's and oz's cancel and, multiplying both side by 100/6, we get
\(\displaystyle x = \frac{30400}{6} \) ~ 5066.67
Again, since the units came out right, you feel a little more comfortable about the answer.

Now you already have 3800 gallons, so you need to add (5066.67 - 3800) gal = 1266.67 gal
 
A logic.

smcelhaney said:
How much water do I need to add to an existing 3800 gallons of a tank mix with a chemical at an 8 oz/100 gallon ratio to make it a 6 oz/100 gallon mix?
Click to expand...

If 100 gallons contains 8 oz of salt then 3800 gallons contains 38(8) = 304 oz of salt.

If 100 gallons of water must be added to 6 oz of salt, then, proportionally, (304/6) times as much water must be added to the 304 oz of salt, (100)(304/6) = 5066.67 gal.

Since 3800 gallons has already been added to the 304 oz of salt, you only need add 5066.67 - 3800 = 1266.67 gallons of water.
 
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