Question

A CARPENTER SAWED A PIECE OF WOOD INTO 3 PIECES. THE RATIO OF WOOD PIECES IS 1:3:6. THE LONGEST PIECE IS 2.5 FEET LONGER THAN THE SHORTEST PIECE. USE THE DRAW A DIAGRAM STRATEGY TO FIND THE LENGTH OF THE ORIGIANL PIECE.

Answer 1

Answer: Hello there!

we know that the ratio of the pieces is 1:3:6

this means that the longest one has 3 times the length of the middle one and 6 times the length of the shortest.

we also know that the longest piece is 2.5 feet longer than the shortest piece, and we want to find the length of the original piece.

ok, let's define L as the length of the longest piece, M for the middle one and S for the shortest piece; then:

1) L - S = 2.5

2) L = 6*S

3) L = 3*M

we could replace the second equation into the first equation and get:

L - S = 2.5 ft

6S - S = 2.5 ft

5S = 2.5 ft

S = 2.5 ft/5 = 0.5 feet

now we can replace the value of S in the second equation and get the value of L.

L = 6*S = 6*0.5 ft = 3ft

and now we can replace the value of L in the third equation and get the value of M

L = 3M

3ft = 3M

M = 3ft/3 = 1ft

then L = 3ft, M = 1ft and S = 0.5ft

then the total lenght is L + M + S = 4.5 ft

Answer 2

1 : 3 : 6

longest piece is 2.5 longer than the shortest piece.

let x be the shortest piece.

x + 2.5 is the longest piece

x/10 + 3/10 + (x+2.5)/10 = 1
x + 3 + x + 2.5 / 10 = 1
2x + 5.5 = 10
2x = 10 - 5.5
2x = 4.5
x = 4.5/2
x = 2.25 shortest piece.

x + 2.5 = 2.25 + 2.5 = 4.75 longest piece.

ratio of the 2nd piece to the 3rd piece is 3:6
2nd piece is half of the 3rd piece

4.75 x 1/2 = 2.375

1 : 3 : 6
2.25 : 2.375 : 4.75