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Topic: Can someone help me with a math question?**Question:**
this is a self taught class so please no crap about doing it myself. I already am.
Miss Bass manages a herbicide plant. she wants a solution of 61% herbicide to be mixed with a solution of 50% herbicide to form 44 liters of a 53%solution. How many liters of the 61% solution must Miss Bass use?
Please not just the answer; I would like to know how to solve this type of problem on my own.

July 18, 2019 / By Dalinda

You do these types of problems via mass balance. That is, the amount of herbicide in the solutions you mix is equal to the amount of herbicide in the final mixture. Next we have to assume what your percentages mean: they could be based on volume or they could be based on mass. Let's assume they're based on volume because gthis will make the problem easier. Let S be the volume of 61% herbicide solution. Then 0.61S must be the amount of herbicide in the solution. Let D be the volume of 50% herbicide solution. Then 0.5D must be the amount of herbicide in this solution. The total amount of herbicide is 0.61S + 0.50D Now look at the final mixture. It contains 53% herbicide. Since there are 44 liters, then the herbicide is 0.53*44 = 23.32 liters of herbicide. This amount must equal what went in 0.61S + 0.50D = 23.32 So far, so good. But we have 1 equation with 2 unknowns. We need another equation. That equation mus be that the total mix must be the sum of the total from the two smaller amounts S+D = 44 You now have two equations and 2 unknowns. You can solve this by multipying the second equation by 0.5 and then subtracting it from the first: 0.61S + 0.50D = 23.32 0.5S + 0.5D = 22 ___________________ 0.11S = 1.32 S = 12 liters S referred to the 61% solution so we're done.

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Did you like the answer? As derived from the theorem of Pascal's Triangle, there are 3 basic rules/laws of quadratic equations which are namely: 1. (a + b)(a - b) = (a² - b²) 2. (a + b)² = a² + 2ab + b² 3. (a - b)² = a² - 2ab + b² When all the above is not applicable, you use the FOIL (First, Outer, Inner, Last) method, the slow factorisation method, which currently applies to your given question. Solution: (t + 3)(t - 4) = t² - 4t + 3t - 12 = t² - t - 12 Multiply the first term of (t + 3), which is t, by the first term of (t - 4), which is t. You get t². Then multiply the outer term of (t + 3), which is t, by the outer term of (t - 4), which is -4. You get -4t. Next, multiply the inner term of (t + 3), which is 3, by the outer term of (t - 4), which is t. You get 3t. Lastly, multiply the last term of (t + 3), which is 3, by the last term of (t - 4), which is -4. You get -12. It's just following patterns. It's so hard to explain through writing. I hope you've understood though.

( t + 3 ) ( t - 4 ) = t.t - 4.t + 3.t - 12 = t^2 - 4t + 3t - 12 = t^2 - t - 12 i hope i remember right.

I think what you would do for this is set up a proportion. 44/.53 = X/.61 This is because 44 L is 53% solution. SO we need to know 61% solution. The next step is cross multiplying. 44(.61)=.53X When doing this you get X= 50.64 L

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The total number of liters of solution is 44. Let x be the number of liters of 61% solution so (44 - x) is the number of liters of 50% solution 0.61x + 0.50(44 - x) = 0.53(44) 0.61x - 0.50x + 22 = 23.32 0.11x = 1.32 x = 1.32 / 0.11 = 12 So she needs 12liters of 61% solution (and 32 liters of 50%)

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10 children * 6 Eggs= 60 eggs total 60/4=15, fifteen is one fourth of 60. three fourths would be 45. 60-45=15. 15 eggs are left!

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