Printer toner coverage

Question

I have a printer that I used for $2$ years. First year I printed $9630$ pages, with $17\%$ ink coverage per page. Ink coverage is the percent of the page that is not white. Second year I printed $1660$ pages with $x\%$ coverage. Total for two years I printed $11290$ pages with an average coverage of $14\%$. In year $2$ the coverage fell below $17\%$ obviously, but how much was it?

score 5 · Answer 1 · answered Dec 16 '14 at 20:16

This is impossible. Printing $9630$ pages with $17\%$ coverage is equivalent to printing $9630\cdot0.17=1637.1$ full pages. Printing $11290$ pages with $14\%$ coverage is equivalent to printing $11290\cdot0.14=1580.6$ full pages. This means that you printed more in the first year than you did in the first and second year combined, which doesn't make sense, as I don't see how you can print negative pages. (In the mathematical sense, not the photographic sense).

...perhaps the printer sucked the ink off the page in year #2. — vadim123, Dec 16 '14 at 20:29

score 2 · Answer 2 · edited Apr 13 '17 at 12:19

2

Imagine it in terms of total pages of ink printed. In that case you have $$\text{total ink year 1}+\text{total ink year 2}=\text{total ink}\\9630\times0.17+1660\times x=11290\times0.14$$ and solve for $x$.

ETA: And... it appears this situation is impossible. See KSmarts answer.

edited Apr 13 '17 at 12:19

Community

1

answered Dec 16 '14 at 20:10

turkeyhundt

7,733

This gives $x\approx-3.4%$. – KSmarts Dec 16 '14 at 20:17
Ha. I didn't work it out. Then it appears we have an impossible situation :) – turkeyhundt Dec 16 '14 at 20:19

Printer toner coverage

2 Answers2