son said:

Baseball outs : In a game, 12 of a baseball team's 27 outs were fly balls. 25% of the outs made by infielders and 100% of the outs made by the outfileders were fly balls.

a) Write a linear system you can use to find the number of outs made by infielders and the number of outs made by outfielders. (Hint: Write one equation for the total number of outs and another equation for the number of fly ball outs)

b) How many outs were made by infielders How many outs were made by outfielders?

The first step is to NAME things.

You are looking for the outs made by infielders, and the outs made by outfielders. So, let's define variables to represent each of those:

let x = outs made by the infielders

let y = outs made by the outfielders

Now...what does the problem say? There were 27 outs! So,

outs made by infielders + outs made by outfielders = total number of outs

x + y = 27

We also know that 12 of those outs were on fly balls, and we know that 25% of the outs made by infielders and 100% of the outs made by outfielders were on fly balls.

If the inflielders made x outs, and 25% of them were on fly balls, then the number of outs made by infielders on fly balls is 25% of x, or 0.25x.

If the outfielders made y outs, and 100% of them were on fly balls, then the number of outs made by outfielders on fly balls is 100% of y, or 1.00y, or y.

outs made by infielders on fly balls + outs made by outfielders on fly balls = total outs on fly balls

There were 12 outs made in all on fly balls. 0.25x were made by the infielders, and 1.0y or xy, were made by outfielders.

.25x + y = 12

So...you have two equations in two variables:

x + y = 27

.25x + y = 12

That is the system you need to solve.

Once you have the value for ONE of those variables, you can easily find the value of the other.