A 32 inch board is cut into three pieces. The second piece is twice as long as the first, and the third piece is five times as long as the second. Find the length of all three pieces in inches.
2007-07-01 06:43:13 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
This is so easy!!!
The three lengths in inches are:
20
8
4
2007-07-01 06:49:54 · answer #1 · answered by ask lylah 3 · 2⤊ 1⤋
Hi,
If the 1st piece has a length of x, then the second piece is twice that, or 2x. The third piece is 5 times the second piece so that's 5(2x) or 10x.
All 3 pieces must add up to 32", so x + 2x + 10x = 32
13x = 32
x = 32/13"
2x = 64/13"
10x = 320/13"
I hope those help!! :-)
The pieces are 32/13", 64/13" and 320/13".
2007-07-01 13:47:32 · answer #2 · answered by Pi R Squared 7 · 1⤊ 1⤋
Let the three board lengths be x, y, z. Then we have 3 equations:
x + y + z = 32
y = 2x
z = 5y
Substitute z = 5y into the first equation
x + y + 5y = 32
x + 6y = 32
Now substitute y = 2x into this equation
x + 6(2x) = 32
x + 12x = 32
13x = 32
x = 32/13
So y = 2(32/13) = 64/13
and z = 5(64/13) = 320/13
The three board lengths are 32/13 inches, 64/13 inches, and 320/13 inches.
2007-07-01 13:50:21 · answer #3 · answered by pki15 4 · 1⤊ 1⤋
You have 3 pieces that add up to 32 inches.
Relate each piece to the other
The three pieces are the first , x
The second is 2x
The third is 5 (2x) = 10x
Add all 3. So x + 2x + 10x = 32
13x = 32
x = 2.46 inches
2x = 4.92 inches
10x = 24.62 inches
2007-07-01 13:45:27 · answer #4 · answered by ignoramus 7 · 0⤊ 5⤋
ok... it would be something like this...
T=total
M=1st piece
N=2nd piece
X=3rd piece
T=32 in
N=2M
X=5N
32=(N/2)+2M+5N solving this one you get
4/11(16-M)=N
Combining equations
4/11(16-M)=2M solving for M
32/13=M
So the length of the 1st piece is 32/13 and then substitute in the 1st equations
N=2(32/13)= 64/13
X=5(64/13)= 320/13
T=(32/13)+(64/13)+(320/13)=32
2007-07-01 14:10:26 · answer #5 · answered by Anonymous · 1⤊ 0⤋
Let x = length of first piece. Then:
x + 2x + 5(2x) = 32
x + 2x + 10x = 32
13x = 32
x = 2.46
2007-07-01 13:47:24 · answer #6 · answered by Runa 7 · 0⤊ 1⤋
4 inches, 8 inches, and 20 inches? I had a horrible algebra teacher in h.s., I was in an accelerated class and we all passed on a red F. He had us so confused. I swear my brain is still scarred to this day!
2007-07-01 13:54:40 · answer #7 · answered by ? 4 · 0⤊ 2⤋
x + 2x + 10x = 32
13x =32
x = 2.46
so first piece is 2.46 inches
second is 2 x 2.46 = 4.92nches
third is 5 x 4.92 = 24.6inches
2007-07-01 13:47:25 · answer #8 · answered by sweet n simple 5 · 1⤊ 1⤋