Question

Last softball season, Pamela had 46 hits, a combination of singles (1 base), doubles (2 bases), and triples (3 bases). These 46 hits totaled 66 bases, and she had 4 times as many singles as doubles. How many doubles did she have?

Answer 1

She had 8 doubles.

Explanation:

This question is solved by a system of equations.

I am going to say that:

x is the number of singles.

y is the number of doubles

z is the number of triples.

46 hits

This means that
`x + y + z = 46`

46 hits totaled 66 bases

This means that:

`x + 2y + 3z = 66`

4 times as many singles as doubles

This means that
`x = 4y`

So

`x + 2y + 3z = 66`

`4y + 2y + 3z = 66`

`6y + 3z = 66`

And

`x + y + z = 46`

`4y + y + z = 46`

`5y + z = 46 \rightarrow z = 46 - 5y`

Then

`6y + 3z = 66`

`6y + 3(46 - 5y) = 66`

`6y + 138 - 15y = 66`

`9y = 72`

`y = (72)/(9)`

`y = 8`

She had 8 doubles.