Answer:
9, 15, 4, 36
Step-by-step explanation:
You want four parts totaling 64 such that 3 added, subtracted, multiplying, and dividing the four parts, respectively, gives equal values.
Let a, b, c, d represent the four parts. Then we have ...
a + b + c + d = 64
a +3 = b -3 = 3c = d/3
Multiply the second equation by 3:
3a +9 = 3b -9 = 9c = d
Now, solve for each of the other variables in terms of d:
a = (d -9)/3
b = (d +9)/3
c = d/9
Substitute these values into the first equation:
(d -9)/3 +(d +9)/3 +d/9 +d = 64
16d/9 = 64 . . . . . . . . collect terms
d = (9/16)(64) = 36
Then the other values are ...
a = (36 -9)/3 = 9
b = (36 +9)/3 = 15
c = 36/9 = 4
The four parts are 9, 15, 4, and 36.
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Additional comment
The value after modification in each case is 12. (9+3=12, 15-3=12, etc.)
It might be easier to write the equation in terms of 'a' or 'b'.
a +(a +6) + (a/3 +1) + (3a+9) = 64 ⇒ 16a/3 +16 = 64 ⇒ a = 3/16(48) = 9