Question

An archer misses the target on her first shot and hits the target on the next 3 shots. what is the least number of consecutive shots that she now must make in order to hit the target on more than 9/10 of al; her shots?

Answer 1

75% to 90%

6

Answer 2

wait >6 because you stated more than 90%

Answer 3

So right now, as of the 4th shot, her ratio is:
\[\frac{3}{4}\]
; 3 hits, 4 shots total. she needs to hit the 'x' shots to raise her total, so lets add x to the top and bottom of that fraction, and we want that to be greater than 9/10:
\[\frac{3+x}{4+x} > \frac{9}{10}\]
Cross mutiplying we get:
\[10(3+x)>9(4+x) \Rightarrow 10x+30>9x+36 \Rightarrow x > 6\]