SOLUTION: In a nine inning game, 17 of a baseball team's 24 outs were fly balls. Fifty percent of the outs made by infielders and 100% of the outs made by outfielders were fly balls. a) How

Question 325140: In a nine inning game, 17 of a baseball team's 24 outs were fly balls. Fifty percent of the outs made by infielders and 100% of the outs made by outfielders were fly balls. a) How many outs were made by the infielders? b) How many outs were made by the outfielders?
Found 2 solutions by vleith, Theo:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
This is a really poor question.
I suspect the problem expects you to use the following logic.
There were 24 outs, of which 17 were fly balls. So that leaves 7 groundball outs.
If that is the case, then the infielders made 7 groundball outs. If their out totla had 50% flyball outs, that means the infield had the same number of groundball outs as flyball outs (7). Total 14 infield outs.
If you subtract the 7 infield fly outs from the total fly outs, (17-7) that means there were 10 outfield fly outs.
So why is the is a poor question?
Because there was nothing in the question to say that the 7 outs that were not fly outs were, in fact, ground outs to the infield. What about Strikeouts? What about runners caught stealing? What about all the other wierd sorts of outs that 'can' happen in baseball.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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:

infield fly outs: 7 infield ground outs: 7 outfield fly outs: 10 outfield ground outs: 0 total fly outs: 17 total outs: 24

everything checks out so the answer is good.

Answer is:

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

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