Question

You have $72$ hits in $160$ times at bat. Your batting average is $0.45$. How many consecutive hits must $160$ you get to increase your batting average to $0.56$?

Answer 1

Hint: First of all assume the unknown term the number of consecutive hits need be “h” and then frame the set of equations and then simplify for the resultant required value.

Complete step by step answer:
Let us assume that the number of consecutive hits needed be “h”
By the given data –
${{72 + h}}{{160 + h}} = 0.560$
Perform cross multiplication in the above expression, where the denominator of one side is multiplied with the numerator of the opposite side.
$ \Rightarrow (72 + h) = (160 + h)(0.560)$
Open the brackets and then simplify –
$ \Rightarrow 72 + h = 160(0.560) + h(0.560)$
Multiply the constants with the term inside the bracket –
$ \Rightarrow 72 + h = 89.6 + 0.560h$
Take all the like terms together. When you move any term from one side to another, then the sign of the term also changes. Positive terms become negative and vice versa.
$ \Rightarrow h - 0.560h = 89.6 - 72$
Simplify the above expression –
$ \Rightarrow 0.44h = 17.6$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$ \Rightarrow h = {{17.6}}{{0.44}}$
Simplify the above expression –
$ \Rightarrow h = 40$
Hence, you will need $40$ consecutive hits to move the batting average from $0.450$ to $0.560$

Note: Always read the question twice and frame the word statement in the mathematical form. Segregate all the known and unknown terms and form the corresponding ratios and the proportions accordingly. Be good multiples and divisions and remember till twenty for the accurate and an efficient solution. Always remember that the common factors from the numerator and the denominator cancels each other.