Dear Math Central, I am writing this as a Mom, who has been away from Honors Algebra for many years. Please help, since I am not sure how to tackle this problem. The question involves baseball hits for Jimmy, a team player.

One seventh of Jimmy's hits were doubles
12.5% of his hits were homeruns
Jimmy had 82 singles
He did not have any triples

How many hits did Jimmy have? (Be sure to include the equation that represents the number of hits)

Extra:
In baseball, the statistic called "total bases" measures how many bases a player generates based on their hits. The official formula is:

Hits + Doubles = (Triples times2) + (Home runs times 3)

What is Jimmy's Total Bases Statistic I appreciate any help given, am at a loss.......

Thank-you
Patty

This problem is given at a Freshman level in Honors Algebra Class


Hi Patty,

There are 4 kinds of hits, singles, doubles, tripples and homeruns. Jimmy has no tripples so his hits are either singles, doubles or homeruns. One seventh of his hits are doubles and 12.5% of his hits are homeruns, thus

 1/7 + 12.5% of his hits are doubles or homeruns. 12.5% is  12.5/100 hence the fraction of his hits that are doubles or homeruns is  1/7 + 12.5/100 = 100/700 + 87.5/700 = 187.5/700

The rest of his hits, 82 of them, are singles so the fraction of his hits that are singles is

1 - 187.5/700 =  512.5/700

Let x be the number of hits that Jimmy got, then

 512.5/700 x = 82 Solve for x

Once yopu know x you can find the number of doubles, one seventh of x, and the number of homeruns, 12.5% of x.

The formula in the "Extra" section looks strange. Should it be

Singles + Doubles + (Triples times 2) + (Home runs times 3)?

Penny

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