Question 272475: a 25 foot wire is to be cut so the longer piece is 1 foot longer than 5 times the shorter piece. find both lengths
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The 25-ft wire is cut into two pieces. We can call these 'x' and 'y'. And in algebra, we'd say:
x + y = 25
or
y = 25-x
.
We also are told there is a relationship between the lengths of 'x' and 'y'.
x = 5y + 1 :: 'x' is 1 foot longer than 5 times 'y'
.
substituting y = 25-x, we have
x = 5(25-x) + 1
.
multiplying through
x = 125 - 5x + 1
.
collecting terms
6x = 126
.
dividing by 6
x = 126/6 = 21
.
Since x+y = 25, then
y = 25 - 21 = 4
.
Checking our work
.
Do they sum to 25?
x + y = ??
21 + 4 = 25
Yes
.
Is x = 5*y + 1?
5(4) + 1 = 21 ??
Yes
.
So our answer is:
x = 21 feet
y = 4 feet
.
Done
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