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EleoNora [17]
3 years ago
11

A chemical company makes two brands of antifreeze. The first brand is 60% pure antifreeze, and the second brand is 85% pure anti

freeze. In order to obtain 110 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used
Mathematics
1 answer:
rjkz [21]3 years ago
3 0

Let’s say we have x gallons of brand 1 antifreeze and y gallons of brand 2 antifreeze. We know we need a total of 140 gallons, so one equation to relate the variables would be x+y=140. We also know that our final mixture should have 60% antifreeze, so another equation would be the weighted average of the two brands: .55x+.80y140=.60. (The weighted average is basically multiplying each % (55 and 80) by the number of gallons you have (x and y


) and adding those together, and dividing that by the total number of gallons (140). This equals the % of the final mixture (60).)


Now we have a system of two equations that we can solve.


x+y=140


.55x+.80y140=.60


*rearrange first equation to solve for y


:


y=140−x


*substitute this value in for y


in the second equation:


.55x+.80(140−x)140=.60


*use algebra and solve for x


:


The algebra shouldn’t be too complex, and I’m hoping you’re asking this about the setup rather than the actual algebra, and I’m lazy, and I used a calculator to solve this, and this is probably a long run-on sentence, and I got x=112


.


*plug this in to first equation and solve for y


:


y=140−112=28


x=112,y=28


112 gallons of brand 1 antifreeze, 28 gallons of brand 2 antifreeze. That’s a whole lot of antifreeze.

thanx heyaaaaaa

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