ACT Math 5.5 Elementary Algebra

ACT Math: Elementary Algebra Drill 5, Problem 5. How much 10% solution must be added to yield the correct concentration?

ACT MathElementary Algebra
ACT MathematicsElementary Algebra
AlgebraWord Problems
Elementary AlgebraLinear equations
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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.