SOLUTION: The volumes of two cubes differ by 259 cu meters. If the edges of one cube are each 4 meters greater than the edges of the other, what is the sum of the lengths of one edge of each

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Question 229266: The volumes of two cubes differ by 259 cu meters. If the edges of one cube are each 4 meters greater than the edges of the other, what is the sum of the lengths of one edge of each cube?
Found 2 solutions by checkley77, ankor@dixie-net.com:
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
X^2-Y^2=259
X=Y+4
(Y+4)^2-Y^2=259
Y^2+8Y+16-Y^2=259
8Y=259-16
8Y=243
Y=243/8
Y=30.375 ANS FOR THE SMALLER SQUARE SIDES.
X=30.375+4
X=34.375 ANS FOR THE LARGER SQUARE SIDES.
PROOF:
34.375^2-30.375^2=259
11.81.64-922.64=259
259=259

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The volumes of two cubes differ by 259 cu meters.
If the edges of one cube are each 4 meters greater than the edges of the other,
what is the sum of the lengths of one edge of each cube?
:
Let x^3 = vol of the smaller cube
then
(x+4)^3 = vol of the larger
:
Large cube vol - small cube vol = 259 cu/m
(x+4)^3 - x^3 = 259
:
(x+4)(x^2 + 8x + 16) - x^3 = 259
:
x^3 + 12x^2 + 48x + 64 - x^3 = 259
:
Fortunately the x^3's cancel and we can form a quadratic equation
12x^2 + 48x + 64 - 259 = 0
:
12x^2 + 48x - 195 = 0
:
Simplify divide by 3
4x^2 + 16x - 65 = 0
:
Factor this to
(2x - 5)(2x + 13) = 0
:
Positive solution
2x = +5
x = 2.5 meters is the edge of the smaller cube
then
2.5 + 4 = 6.5 meters is the edge of the larger
:
"what is the sum of the lengths of one edge of each cube?"
2.5 + 6.5 = 9 meters
;
:
Check solution on a calc; enter 6.5^3 - 2.5^3 = 259