The difference between a and 45 is divided by p
Answers
Step-by-step explanation:
[tex]The first part is 8, the second part is 12, the third part is 5, and the fourth part is 20. The number all four operations result in is 10.
This was a pretty basic algebra word problem. The way I learned to do it in school was like this:
First, get it in the form of unreadable henscratches. Algebra teachers love their unreadable henscratches. Representing the four parts as A, B, C, and D, we have the following two equations:
A + B + C + D = 45
A + 2 = B - 2 = 2 * C = D / 2 = E
And then algebra happens [1]. You chase those equations down until you finally catch the number hiding at the end, then you have a cigarette, roll over, and go to sleep.
But that's not how I did it. I hate math, so I just estimated the answer and checked it. Looking at equation two, I noticed that the variables came in complimentary pairs, so I figured the average size of each part should be approximately one quarter of the final sum, 45. But multiplication and division are multiplicative, not additive, inverses, which would make the final sum slightly larger than otherwise, and 45 isn't evenly divisible by 4 anyway, so I rounded down to the largest number smaller than 45 divisible by 8, which is 40. A quarter of 40 is ten. I substituted ten for E in the second equation above, tested it against the first, and lo and behold, it worked.
Incidentally, My elementary school teachers really didn't like it when I solved math problems this way.
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[1] This was the boring process I was supposed to go through:
A = E - 2
B = E + 2
C = E / 2
D = 2 * E
Therefore,
E - 2 + E + 2 + E / 2 + 2 * E = 4 * E + E / 2 = (9 * E) / 2 = 45
Therefore,
E = 10
And the rest follows.
9 * E = 90
A = 10 - 2 = 8
B = 10 + 2 = 12
C = 10 / 2 = 5
D = 10 * 2 = 20
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