Suppose a sheet of 100 stamps is 0.62 millimeters thick. if a stack of sheets contains 10,000,000 stamps, how many millimeters thick is the stack? write the answer in scientific notation.

You can set up a proportion for this. Let x be the thickness obtained by stacking 10 million stamps

100:0.62 : : 10,000,000 : x

Now set it up as a proportion so you can cross multiply.

100/0.62 = 10,000,000/x               Cross multiply

100x = 0.62 * 10,000,000              change 0.62 to a fraction

0.62 = 62 / 100                               Substitute 62/100 into the proportion  

100 x = 62/100 * 10,000,000         Divide by 100  

100 x = 62 * 100, 000                     Multiply by 61

100x = 6,200,000                           Divide by 100 on both sides

x = 6,200,000/100                          62,000 mm

x = 62,000 mm

x = 6.2 * 10^4 mm  answer

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4