Question

Your cell phone company charges $0.50 per megabyte of data with a flat fee of $75. Your friend's company charges $0.80 per megabyte with no flat fee. If you and your friend paid the same amount for the same number of megabytes, how many megabytes did you each use?

Answer 1

if you use 1Mb of data in your cell company, you pay

0.50(1) plus the 75 fee, or 0.50 + 75

for 2Mbs, you pay 0.50(2) + 75

for 3Mbs, 0.50(3) + 75

for "m" Mbs, you pay 0.50(m) + 75.


now, your friend pays only for how many Mbs of she uses,

so for 1Mbs of she pays 0.80(1)

for 2Mbs, 0.80(2)

for 3Mbs 0.80(3)

for "m" Mbs 0.80(m).

now, if you paid say "y", so y = 0.50m + 75


and your friend paid also the same amount, say "y", y = 0.80m

then both amount are equal, what is "m"?


`\bf 0.50m+75=0.80m\implies 75=0.30m\implies \cfrac{75}{0.30}=m\\\\\\ 250=m`