Problem

Liquid mixture problems. The colors on the paint …

06:29

Problem 44 Hard Difficulty

Liquid mixture problems.
One website recommends a $6 \%$ chlorine
bleach-water solution to remove mildew. A chemical lab has
$3 \%$ and $15 \%$ chlorine bleach-water solutions in stock. How
many gallons of each should be mixed to obtain 100 gallons of
the mildew spray?

Answer

$x=75$ gallons

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Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 6

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Video Transcript

four reads. One website recommends a 6% chlorine bleach water solution to remove mildew. A chemical lab is drew percent and 15% chlorine bleach, water solutions and stock. How many gallons of each of the mix obtain 100 gallons of the mildew spray? So starting off, I made a chart that has low high mix, and we're using the equation. Amount time strength is equal to the amount of bleach. So for the low bleach water solution, it's 3%. So as a decimal that's written a 0.3 And then for the high bleach water solution, that's 15%. So as it s small, that 0.15 and then the mixture is 6%. So as it s more leads airplanes. Your six. And we want to know how much of the low bleach and the high bleach it would take to make 100 leaders of the mildew spray or gallons of the multi spray. And so I'm gonna put X to represent the amount of gallons of the low bleach solution and then 100 minus X to represent the amount of the high bleach solution and then from here we have to multiply the amount times the strength to get the amount of bleach. So for the low bleach solution is gonna be 0.3 X and then for the high bleach solution, it's gonna be 0.15 times 100 minus X. And then for the mix, we're gonna multiply 100 times 0.6 and that's just gonna leave us with six. So now we're gonna write a question where we set the amount of bleach of the low and the high bleach solution to equal the amount of bleach and the mixture. Sorry equations. Gonna look something like 0.3 X plus Sarah 0.15 times 100 minus eggs is equal to six. And then from here, we're gonna get rid of the decimals by multiplying both sides of the equation by 100. So we have 100 times their 1000.3 ex, which is just three X and then we have 100 times their 1000.15 which is 15 and we have to multiply the 15 by 100 minus x six times 100 600. From here, we have to distribute the 15 to the 100 as well as the 15 to the negative X. So we have three eggs, plus 15 times 100 is 1500 or 1000 500 and then 15 times negative. X is negative. 15 X is equal to 600 and now it's a combined like terms. So we have three X minus 15 x and three X minus 15 exes. Negative, 12 x So we have negative 12 X plus 1500 is equal to 600. And then we want to get the 1500 to the other side equation to be with the 600. So we're going to subtract 1500 on each side, 1500 minus 1500 crosses out. So the more left with negative 12 X and by crosses out, I mean is equal to zero, so we can cross it out. We have 600 minus 1500 which is negative. 900. And then to get rid of the negative 12 or to isolate the X, we're gonna have to divide both sides by negative 12. So I'm gonna rewrite that part because it got cut off soon. Negative 12 X is equal to negative 900 and we're gonna divide both sides by negative 12. Negative 12. Divided by negative. 12 is one, so we can cross it out and we're left with just X. And then we have negative 900 divided by negative 12 which is 75 positive. 75. So we have 75 gallons of the low bleach solution, which is of the 3% bleach water. And then to figure out how much we have of the high believed water, we have to subtract 100 minus X. So we have 100 minus and in this case, exit 75. So we're just doing 100 minus 75. Ah, 100 minus 75 is 25. So we have 25 gallons of the 15% lead water, and that is our solution to the problem.

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