Using ratios to figure out how to properly mix chemicals

[cesarsiles]

I recently took the written exam for the Los Angeles fire department, and one question stumped me. Here it is: if you are using a ratio of 3:2 and you have to make a 700-gallon mixture of two chemicals, what is the proper mixture?

I know that 3 is 1.5 times more than 2, so I tried dividing 700/1.5 = 466.67 then 700- 466.67= 233.33 to get a mixture of 466.67 to 233.33 at a ratio of 3:2 for a 700 gallon mixture of two chemicals. But 466.67/233.33 doesn’t give me a ratio of 3:2. Please help.

 

[stapel]

if you are using a ratio of 3:2 and you have to make a 700-gallon mixture of two chemicals, what is the proper mixture?

You are making some mixture of input components A and B.

The "ratio of three to two" means that you have three parts one thing and two parts another thing. How many parts is that?

You need to obtain a 700-gallon mixture. If you split that number into the correct number of parts, how many gallons are in one part?

Then how many gallons of each of A and B do you need? :wink:

Eliz.

 

[soroban]

Hello, cesarsiles!

if you are using a ratio of 3:2 and you have to make a 700-gallon mixture of two chemicals,
what is the proper mixture?

Here's my baby-talk approach to these ratios . . .

A ratio of 3-to-2 means: .we have 3 parts of chemical A to 2 parts of chemical B.

You see, chemical A makes up 3 parts of the total of 5 parts.
. . So, chemical A takes up \(\displaystyle ^{\frac{3}{5}}\) of the mixture.
This means chemical B takes up the other \(\displaystyle ^{\frac{2}{5}}\) of the mixture.


There you go!

. . \(\displaystyle \text{Chemical A} \: = \: \frac{3}{5} \times 700 \: = \: 420\text{ gallons}\)

. . \(\displaystyle \text{Chemical B} \: = \: \frac{2}{5} \times 700 \: = \: 280\text{ gallons}\)