a pharmacist needs to obtain a 70% alcohol solution. How many ounces of a 30% alcohol solution should she add t 40 ounces of an 80% alcohol solution to obtain the 70% alcohol solution?
Answers (2)
Get a ruler in your hands. Measure things until you start to understand how a ruler works. Measure some stuff and figure out where the center is. Say you measure a book and it's 7/8" thick. You look at your ruler and see that every eighth is divided into two sixteenths, so obviously half of 7/8" is going to be 7/16". If you write that out you have 1/2 x 7/8 = 7/16. And you notice that 1/2 is divided into 2/4 and then into 4/8 and so on, so you can convert anything to anything by multiplying all the numbers on top and then all the numbers on bottom.
Other rulers are divided into 10 and 100 parts. But an inch is still an inch, so anything on one ruler can be translated to the other ruler. A half inch on one ruler is 5/10 or 50/100 on the other. An eighth inch is just 12.5 marks when you have 100 marks per inch. A metric ruler divides an inch into 25.4 parts, so a half inch would be 12.7 of those parts. Pretty simple, isn't it? Practice this a bit and people will think you went to wizard school.
Percent is simply a ruler with 100 marks. The only confusion is trying to keep track of what the marks represent, since that changes from time to time.
How many ounces of a 30% alcohol solution should she add to 40 ounces of an 80% alcohol solution to obtain the 70% alcohol solution?
40 ounces times 80% -- 40 x 0.8 = 32 ounces of alcohol (and 8 ounces of water)
x ounces times 30% -- 0.3x ounces of alcohol (and 0.7x ounces of water)
Total will be 40 + x ounces, 0.7(40 + x) alcohol and 0.3(40 + x) water
Now there are two ways to analyze this: all the waters should add up, and all the alcohols should add up.
Waters: 0.3(40 + x) = 8 + 0.7x
12 + 0.3x = 8 + 0.7x
4 = 0.4x
x = 10
Alcohols: 0.7(40 + x) = 32 + 0.3x
28 + 0.7x = 32 + 0.3x
0.4x = 4
x = 10 <-- SAME ANSWER
2) batman can clean the area in 8hr working alone. Robin would take 12 hr. if robin starts at 8 am and batman joins him at 10 am, at what time will they finish?
A = area
Batman cleans (1/8)A in 1 hour. Robin cleans (1/12)A in 1 hour.
LCM (8, 12) = 24
1/8 = 3/24
1/12 = 2/24
In 2 hours (8 am to 10 am) Robin cleaned 2/12 = 4/24 of the area.
So, 5/6 = (20/24)A have yet to be cleaned.
5/6 = x( 1/8 + 1/12 )
20/24 = x (3/24 + 2/24)
20 = 5x
x = 4
In 4 hours (10 am to 2 pm) R&B will have cleaned the remaining area.