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

ACT Math | Elementary Algebra |

ACT Mathematics | Elementary Algebra |

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Okay, It's all about concentration levels... like in a sports drink, really.

Like... ever cut a bottle of Gatorade with water? Same idea.

Let's say we just finished a brutal 2 on 1 against Kobe and Lebron and sweated 2.5 liters.

The "watered down" Gatorade has 4% sugar; and the normal Gatorade has 10% sugar.

We're sorta like the 3 bears in this sense -- we want the porridge neither too hot nor

too cold...

...the Gatorade has to be somewhere in between the 4 and the 10, and we think 6% is about

the right concentration to replace the electrolytes we lost dragging Kobe and Lebron up and down the court.

To help frame even further

Now let's do the math. We can write 2.5 liters of 4% solution as

2.5 times .04, which is 0.1.

Monty has x liters of 10% solution, so x times .1 is .1x.

Together, the 6% solution will have 2.5 liters plus x, which we can write as .06 times the

quantity 2.5 plus x.

Distributing the .06...we have .15 plus .06x. So if we set up the equation... 0.1 plus 0.1x

equals .15 plus .06x. Combining like terms...which means grouping

the x's together and the constants together, we get that .04x equals .05.

Divide both sides by .04, and x equals 1.25, or 1 and 1/4 liters...

Looks like B is our answer.