Question

55. You have 35 hits in 140 times at bat. Your batting average is 35/140 or 0.25. How many consecutive hits must you get to

increase your batting average to 0.3?

Answer 1

Explanation:

The current situation is computed by 35/140 = 0.25

The best possible way to raise the average is to get all 'hits' until the average is 0.3

That looks like this, if it takes 'x' more tries (all hits) to get to a 0.3 average (see below)

(35 + x)/(140 +x) = 0.3

The 'secret' to this problem is that you must add the same number to both the numerator and denominator of the fraction and get a result of 0.3

So, we use the equation (35 + x)/(140 +x) = 0.3.

Multiply both sides by the denominator of (140 + x) on the left, to clear the fraction.

35 + x = 0.3(140 + x)

35 + x = 42 + 0.3x

x + 35 = 0.3x + 42

Subtract 0.3x from both sides

0.7x + 35 = 42

Subtract 35 from both sides

0.7x = 7

Divide both sides by 0.7

x = 7/0.7 =10

x = 10

If this is correct, then changing 35/140 to 45/150 should give us 0.3

In fact, 45/150 reduces to 9/30 reduces to 3/10 = 0.3, so that looks good.

I hope this helps.