Question

Mr. Cruz cut three pieces of wood for a project. The first piece of lumber is the longest. The second piece is 7/8 times as long as the first piece. The third piece is 12 5/16 inches shorter than the second piece. The third piece is 24 7/16 inches long.

a. How long is the first piece of wood?

b. How much wood did Mr. Cruz use to make all 3 pieces?

c. Mr. Cruz has 32 feet of lumber left. He wants to cut 4 more of each of the pieces described above. Does he have enough lumber? Justify the answer.

Answer 1

x = first piece
y = 2nd piece
z = 3rd piece

x is the longest
y = 7/8x
z = y - 12 5/16 which = 7/8x - 12 5/16
z = 24 7/16

7/8x - 12 5/16 = 24 7/16
7/8x - 197/16 = 391/16
7/8x = 391/16 + 197/16
7/8x = 588/16
x = 588/16 * 8/7
x = 4704/112
x = 42

y = 7/8x
y = 7/8(42)
y = 294/8
y = 36 3/4

x = 42
y = 36 3/4
z = 24 7/16

any questions ?

Answer 2

a) first piece of wood is 42

b) all three pieces (42 + 36 3/4 + 24 7/16)
42 + 36 + 24 = 102
3/4 + 7/16 = 12/16 + 7/16 = 19/16 = 1 3/26
102 + 1 3/16 = 103 3/16 <-- total

c) he has 32 feet of lumber
4(103 3/16) = 4 * 1651/16 = 6604/16 = 412 3/4
412.75/12 = 34.40 ft.
He does not have enough