Question 325140
24 total outs.
17 were fly balls.
7 were not fly balls.
50% of the outs were made by infielders.
50% of the outs were made by outfielders.
100% of the outs made by outfielders were fly balls.


50% of the outs made by infielders were fly balls.
100% of the outs made by outfields were fly balls.


infielders made 12 outs.
outfielders made 12 outs.


Let x = the total outs made by infielders
Let y = the total outs made by outfielders.


You have a total of 24 outs which means that x + y = 24


You know that 50% of the outs made by infielders and 100% of the outs made by outfielders were fly outs.


This means that .5*x + y = 17


You have 2 equations that need to be solved simultaneously.


They are:


x + y = 24
.5x + y = 17


You can use the first equation to solve for x in terms of y, or to solve for y in terms of x.


I'll solve for y in terms of x to get:


Start with:
x + y = 24
Subtract x from both sides of the equation to get:
y = 24 - x


Substitute for y in the second equation to get:


Start with:
.5x + y = 17
Substitute for y to get:
.5x + (24-x) = 17
Simplify to get:
.5x + 24 - x = 17
Combine like terms to get:
-.5x + 24 = 17
Add .5x to both sides of the equation and subtract 17 from both sides of the equation to get:
24-17 = .5x
Combine like terms to get:
7 = .5x
Divide both sides of the equation by .5 to get:
14 = x which is the same as:
x = 14


You have x = 14
From the first equation of x + y = 24, you get:
y = 10 because x + y = 24 (14 + 10 = 24).


x represents total outs made by infielders.
y represents total outs made by outfielders.


infielders made a total of 14 outs of which 50% were fly outs.


this means infielders made a total of 7 fly outs and 7 ground outs.


outfielders made a total of 10 outs of which 100% were fly outs.


this means outfielders made a total of 10 fly outs and 0 ground outs.


add them up together and you get a total of:

<pre>
infield fly outs:            7
infield ground outs:         7
outfield fly outs:          10
outfield ground outs:        0

total fly outs:             17
total outs:                 24
</pre>

everything checks out so the answer is good.


Answer is:


infielders made a total of 14 outs.
outfielders made a total of 10 outs.