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horrorfan [7]
3 years ago
15

The average of two numbers is twice the positive difference between if the smaller number is 9 what's my answer?

Mathematics
1 answer:
Lana71 [14]3 years ago
7 0
Let b, be the smallest number :Note the average of a+b = (a+b)/2
(a+b)/2 = 2(a-b)
a+b = 4(a-b)
a+b = 4a - 4b, but b = 9, then plug:
a+9 = 4a - 36
-3a = -45
3a = 45
and a = 15
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Step-by-step explanation:

Let's say that the Lewis family sprinklers were out for L hours and the Martin family's sprinklers were out for M hours. We know that for each hour that the Lewis family sprinkler was on, 30L of water was put out. We can thus write the Lewis family sprinkler water output as 30L per each hour of L = 30 * L. Similarly, the Martin family sprinkler water output = 15 * M .

We know that the total hours for the sprinklers is 55, so L + M = 55. The total water output for the sprinklers is the sum of the sprinkler outputs, so 30 * L + 15 * M = 1350

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30 * L + 15 * M = 1350

One way to solve this would be to solve for L in the first equation and substitute that into the second

subtract M from both sides in the second equation

55 - M = L

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30 * 55 - 30 * M + 15 * M = 1350

1650 - 15M = 1350

subtract 1650 from both sides to isolate the M and its coefficient

-15M = -300

divide both sides by -15 to isolate M

M = 20

L = 55-20 = 35

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