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CAHSEE Mathematical Reasoning: Drill 1, Problem 1. Based on this information, which of the following can be determined?
CAHSEE Math Mathematical Reasoning: Drill Set 1, Problem 2. Which of the following should be the most appropriate first step in solving the equation?
CAHSEE Math Mathematical Reasoning: Drill 1 Problem 3. Which of the following is the correct order of steps?
ACT Math 5.5 Elementary Algebra 326 Views
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Description:
ACT Math: Elementary Algebra Drill 5, Problem 5. How much 10% solution must be added to yield the correct concentration?
- Elementary Algebra / Linear equations
- Product Type / ACT Math
- Foreign Language / Arabic Subtitled
- Foreign Language / Korean Subtitled
- Foreign Language / Chinese Subtitled
- Foreign Language / Spanish Subtitled
- Mathematics and Statistics Assessment / Word Problems and Applications
- Pre-Algebra / Data collection, representation, and interpretation
Transcript
- 00:03
Time to get your shmoop on...
- 00:05
Monty has 2.5 liters of a 4% solution and
- 00:08
one container of 10% solution. How much 10% solution does he need to add
- 00:14
to the 2.5 liters of the 4% solution to get a 6% solution?
- 00:19
And here are the potential answers...
Full Transcript
- 00:26
Okay, It's all about concentration levels... like in a sports drink, really.
- 00:30
Like... ever cut a bottle of Gatorade with water? Same idea.
- 00:34
Let's say we just finished a brutal 2 on 1 against Kobe and Lebron and sweated 2.5 liters.
- 00:40
The "watered down" Gatorade has 4% sugar; and the normal Gatorade has 10% sugar.
- 00:46
We're sorta like the 3 bears in this sense -- we want the porridge neither too hot nor
- 00:50
too cold...
- 00:51
...the Gatorade has to be somewhere in between the 4 and the 10, and we think 6% is about
- 00:57
the right concentration to replace the electrolytes we lost dragging Kobe and Lebron up and down the court.
- 01:02
To help frame even further
- 01:03
Now let's do the math. We can write 2.5 liters of 4% solution as
- 01:10
2.5 times .04, which is 0.1.
- 01:12
Monty has x liters of 10% solution, so x times .1 is .1x.
- 01:17
Together, the 6% solution will have 2.5 liters plus x, which we can write as .06 times the
- 01:26
quantity 2.5 plus x.
- 01:28
Distributing the .06...we have .15 plus .06x. So if we set up the equation... 0.1 plus 0.1x
- 01:37
equals .15 plus .06x. Combining like terms...which means grouping
- 01:42
the x's together and the constants together, we get that .04x equals .05.
- 01:49
Divide both sides by .04, and x equals 1.25, or 1 and 1/4 liters...
- 01:55
Looks like B is our answer.
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