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

Answer:

She had 8 doubles.

Step-by-step 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

$6y + 3z = 66$

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

$6y + 138 - 15y = 66$

$9y = 72$

$y = \frac{72}{9}$

$y = 8$

She had 8 doubles.