Question

A baseball player reaches base 35% of the time. How many times can he expect to reach base in 850 at-bats?

Answer 1

Hint: This problem can be solved by the method of direct proportion. We will equate the ratio of one time for reaching base with the times on base to at-bats. 35% has to be converted into fraction. For direct proportion, if one quantity increases, it causes a corresponding increase in the other quantity as well or vice- versa.

Complete step-by-step solution:
Now, let’s discuss this particular problem.
As we already know about the direct and inverse proportion. Proportion refers to the ratio. When we say direct proportion, it means if one quantity increases, it causes a corresponding increase in the other quantity as well or vice- versa. On the other hand, inverse proportion means if one quantity increases, the other corresponding to it decreases. Here in this question, we have to apply direct proportion as the base increases, the times to reach at-bats also increase. So, we will equate the ratio of one time for reaching base with the times on base to at-bats.
Now, simply remove the percent and make it a ratio by converting it into a fraction:
$\Rightarrow 35\%\Leftrightarrow \dfrac{35}{100}$
This ratio will be equal to the times on base to at-bats.
$\Rightarrow \dfrac{35}{100}=\dfrac{x}{850}$
Here, ‘x’ is taken as the times which we have to expect to reach base in 850 at-bats. Now, perform cross multiplication:
$\Rightarrow 35\times 850=x\times 100$
Now, solve for x by taking all the constants on one side:
$\Rightarrow \dfrac{35\times 850}{100}=x$
Reduce the terms into simplest form. First divide 100 and 850 by 5, we will get:
$\Rightarrow \dfrac{35\times 17}{2}=x$
On multiplying 35 by 17 we will get 595:
$\Rightarrow \dfrac{595}{2}=x$
Hence the value of ‘x’ will be:
$\therefore $x = 297.5
This is the final answer.

Note: There is one alternate method also which is used as a shortcut. In that method, you can multiply directly the percent by the number of at-bats by converting the at-bats into decimal like decimal form of 35% is:
$\Rightarrow \dfrac{35}{100}\Leftrightarrow 0.35$
After this, multiply with the number of at-bats:
$\Rightarrow 0.35\times 850$ = 297.5
So we got the same answers. All you need to remember the direct and inverse proportions.