Jeff wanted to enlarge a drawing on a copy machine. He first enlarged the original by 30%. He then took the copy machine enlarging it by 30%. He did this 3 more times. if the original drawing had been 2 inches by 3 inches, did the final copy fit on a sheet of paper 81/2 inches by 11 inches? Explain your answer. Can you guess?
2007-04-17 14:17:07 · 7 answers · asked by Dina 2 in Science & Mathematics ➔ Mathematics
So he enlarged it a total of five times?
Enlarge once: d + .3d = 1.3d
Twice: 1.3d + .3*1.3d = 1.3*1.3d
Thrice: 1.3*1.3*1.3d
Four times: (1.3^4)*d
Five times: (1.3^5)*d
So the dimensions of the final copy were 3.71293 * (2 by 3) = a bit less than 7.5 by a bit more than 11 inches.
So no, the final copy did not (quite) fit on a standard sheet of paper. The final copy was also quite a bit degraded in quality, whereas if he'd just enlarged the original by 366%, he'd have ended up with an enlargement that fit on the paper AND wasn't degraded AND didn't waste four sheets of paper. But that's math problems for you. :)
2007-04-17 14:34:00 · answer #1 · answered by Marti 2 · 2⤊ 0⤋
Well, if he took the copy machine .. and enlarged it by 30%.. I am pretty sure it would not fit on any ordinary sheet of paper :).
However, if he took the copy he made originally and enlarged it four times after the first enlargement (I am counting 5 enlargements in all, yes?)
Then, no.. it would be just barely too big.
2(1.30)^5 is approximately 7.4 inches
3(1.30)^5 is approximately 11.1 inches
2007-04-17 21:27:40 · answer #2 · answered by suesysgoddess 6 · 3⤊ 0⤋
Each copy is 1.3 times larger than the previous. If he did it 4 times he would have (1.3)x(1.3)x(1.3)x(1.3)x(1.3)x(a dimension of the original). That makes it, after the multiplication, 2.856 times larger.
For the width of 2" that makes it 5.7 inches wide so that will fit on the paper width.
For the length of 3" that makes it 8.57 inches long so that will fir on the paper length.
IF the original had been about 3" wide it would not have fit. If it had been 4" long it would not have fit.
2007-04-17 21:29:13 · answer #3 · answered by Rich Z 7 · 0⤊ 2⤋
(1.3)^4 = 2.86 the enlargement factor
final dimensions:
2"(2.86)= 5.72"
3"(2.86)= 8.58"
yes, the final copy will fit.
2007-04-17 21:25:41 · answer #4 · answered by jaybee 4 · 0⤊ 1⤋
Why didn't Jeff just draw a bigger picture to begin with? What a moron.
2007-04-17 21:21:41 · answer #5 · answered by jrome 2 · 1⤊ 1⤋
2*1.3^5=7.42
3*1.3^5=11.13
yes it would fit
2007-04-17 21:21:47 · answer #6 · answered by leo 6 · 1⤊ 1⤋
To get our braining going or to do your HW?
2007-04-17 21:20:59 · answer #7 · answered by Virgo27 6 · 0⤊ 2⤋