SOLUTION: A ten-foot-long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4 1/2 feet longer than the second. How long is the first piece?

Question 81657: A ten-foot-long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4 1/2 feet longer than the second. How long is the first piece?

A. 1 1/10 feet
B. 2 1/5 feet
C. 2 3/4 feet
D. 3 1/3 feet

Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
Piece #1 + Piece #2 + Piece #3=10 feet
.
Piece #1=x
Piece#2=1/2x=0.5x
Piece#3=.05x+ 4 1/2=.05x+4.5
Total board = 10
.
Piece #1 + Piece #2 + Piece #3=10 feet [plug-in the values and solve for x]
(x)+(0.5x)+(0.5x+4.5)=10
2x+4.5=10
2x+4.5-4.5=10-4.5
2x=5.5
2x/2=5.5/2
x=2.75 [plug- this back into the original equation]
.
(x)+(0.5x)+(0.5x+4.5)=10
(2.75)+(0.5)(2.75))+(0.5)(2.75)+4.5)=10
10=10 [checks out]

RELATED QUESTIONS
a 48 foot board is cut into three pieces. how long is each piece if the second piece is 3 (answered by josgarithmetic)

A 98 centimeter board is cut into three pieces. The first piece is twice as long as the... (answered by solver91311,macston)

A 9-foot board is cut into three pieces. The second piece is twice as long as the first... (answered by jorel1380)

A 64 inch board is cut into 3 pieces. The second piece is three times as long as the... (answered by Nate)

a 49inch board is to be cut into three pieces so that the second piece is twicw as long... (answered by solver91311,macston)

A 57-foot wire is cut into three pieces. The second piece if 7 feet longer than the first (answered by Boreal,stanbon)

A 20-ft board is cut into three pieces. The second piece is three times as long as the... (answered by stanbon,MathLover1)

A board, 44 cm long is cut into three pieces such that the second piece is twice as long... (answered by algebrahouse.com)

A board, 39 cm long is cut into three pieces such that the second piece is twice as long... (answered by addingup)