SOLUTION: 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

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
RELATED QUESTIONS
A 25-foot wire is to be cut so that the longer piece is one foot longer than 5 times the... (answered by drj)

An 18-foot wire is to be cut so that the longer piece is 5 times longer than the shorter... (answered by stanbon)

A 24 foot wire is to be cut so that the longer piece is three times longer than the... (answered by Alan3354)

A 16-foot piece of string is cut into two pieces so that the longer piece is 1 foot... (answered by Edwin McCravy)

please tell me if this answer is correct. a 25 foot beam is to be divided so that the... (answered by dabanfield)

a 15-foot piece of string is cut into two pieces so that the longer piece is 3 feet... (answered by faceoff57)

A 10 foot board is cut into 2 pieces so that one piece is 2 feet longer than 3 times the... (answered by checkley77)

20-foot piece of string is cut into two peices so that the longer piece is 5 feet longer... (answered by oberobic)

A 17-foot piece of string is cut into two pieces so that the longer piece is 2 feet... (answered by checkley77)