You have 72 hits in 160 times at bat. Your batting average is or 0.45. How many consecutive hits must 160 you get to increase your batting average to 0.56?

Question

1709 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-30T00:57:06

See a solution process below:

We can write the equation to solve this problem as:

#(72 + h)/(160 + h) = 0.560#

Where #h# is the number of consecutive hits need.

Solving for #h# gives:

#color(red)((160 + h)) xx (72 + h)/(160 + h) = color(red)((160 + h)) xx 0.560#

#cancel(color(red)((160 + h))) xx (72 + h)/color(red)(cancel(color(black)(160 + h))) = (color(red)(160) xx 0.560) + (color(red)(h) xx 0.560)#

#72 + h = 89.6 + 0.560h#

#-color(red)(72) + 72 + h - color(blue)(0.560h) = -color(red)(72) + 89.6 + 0.560h - color(blue)(0.560h)#

#0 + (1 - color(blue)(0.560))h = 17.6 + 0#

#0.44h = 17.6#

#(0.44h)/color(red)(0.44) = 17.6/color(red)(0.44)#

#(color(red)(cancel(color(black)(0.44)))h)/cancel(color(red)(0.44)) = 40#

#h = 40#

You will need #color(red)(40)# consecutive hits to move your batting average from 0.450 to 0.560