Raymond B. answered • 04/21/21
Math, microeconomics or criminal justice
6.2 x 80% = 6.2 x 0.80 = 4.96 inches
use a calculator or long hand multiplication
If it were 50% as big, it would be 6.2/2 = 3.1 inches
If it were 75% as big it would be half way between 6.2 and 3.1 or (6.2+3.1)/2 = 9.3/2 = 4.65. 80% is a little bigger than 75%, 4.96 is a little bigger than 4.65
It's 5% bigger. 10% bigger would be 0.62 bigger. 5% is 0.62/2 = 0.31 bigger
add 4.65 to 0.31 = 4.96 inches.
sometimes it helps to work it two ways. IF you get the same answer, odds are very good it's the correct solution. if you just work it the same way twice, that's good too, but sometimes you make the same mistake twice.
6.2 x 0.8 = 49.6 can be checked with the "rule of 9's"
6+2 = 8 8x8 = 64 6+4= 10, 1+0 = 1
the answer should also similarly reduce to 1
4+9+6 = 19, 1+9=10 1+0=1. It's not a perfect check, but odds are at least 90% that you calculated it correctly (in case you don't trust your calculator or long
hand division-----"rule of 9's" are even better with more complicated calculations)
reduce the digits in what you're multiplying, to one digit each. multiply them together. reduce it to one digit. I has to be the same as what you get when you reduce the answer to one digit.
this problem seems like a trick question. why tell you the width? It's an irrelevant distracting number. Unless maybe the question is ambiguous. Maybe it really meant the length is 80% of the area? although that mixes different units making one dimensional units = 2 dimensional units.
But if so, then L = 80% of 6.2(2.6) new length=.8(6.2)(2.6)
L = 12.896 inches
and now you have far more than you ever wanted to know.
This 12.896 solution seems most unlikely, but it's the only way the width 2.6 would be relevant
I'd stick with 4.96 inches
But maybe the problem meant the dollar bill had been reduced 80%, by area
original area was 6.2 x 2.6 = 16.12. 80% of 16.12 = 12.896
old length and width's ratio should equal the reduced length & with ratio
old L/old W = 6.2/2.6 = new L/new W. new W = 12.896/new L
6.2/2.6 = newL/12.896/new L = new L^2/12.896
new L^2 = 12.896(6.2)/2.6
new L = square root of 30.752= about 5.545 inches
I'd still stick with this being a trick question and new length = 4.96
Unless maybe you mis-copied the problem or there's a typo in the problem somewhere.
There is something ambiguous about the way the problem reads. Is 6.2 by 2.6 the old dimensions? or the new reduced dimensions? If the latter, then you want a bigger length for the the original dollar bill before its size was reduced.
If so, then 16.12 is 80% of the original bill's area original area is then 16.12/.8 = 20.15 square inches. 6.2/2.6 = L/W = L/20.15/L = L^2/20.15
L^2 = 6.2(20.15)/2.6 = 48.05
L = sqr480.05 = about 6.93 inches for the original dollar bill's length
Still, I'd stick with 4.96 inches. Other versions seem too complicated. But maybe this is a lesson in making sure you have the correct problem, accurately copied.
