Question

Find \[x\] in the following proportion.\[16:18 = x:96\]

Answer 1

Hint: Solving proportions is a simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross multiplying if needed, and solving the resulting equation. A proportion is an equation that says that two ratios are equivalent. If one number in a proportion is unknown you can find that number by solving the proportion. Which is shown below:

Complete step-by-step answer:
Given, \[16:18 = x:96\]
My first step will be to convert the colon based odds notation to fractional form, so I get an equation with two fractions which we can solve easily. As we have only one unknown variable value among the four values, we can solve this.
\[\dfrac{{16}}{{18}} = \dfrac{x}{{96}}\]
Since we have the unknown value in the numerator, we can easily solve this.
If we have the unknown value in the denominator we convert the proportion equation such that we will get the unknown value in the numerator.
Multiply 96 on both sides, we get
\[ \Rightarrow \dfrac{{16}}{{18}} \times 96 = \dfrac{x}{{96}} \times 96\]
On Cancelling and rearranging we get,
\[ \Rightarrow x = \dfrac{{16}}{{18}} \times 96\]
Using simple multiplication we get,
\[ \Rightarrow x = \dfrac{{256}}{3}\]
If we want we can keep it in fraction form or we can divide it,
So we get,\[ \Rightarrow x = 85.3333\].
We can verify this answer by plugging it back into the original equation.
So, the correct answer is “x = 85.3333”.

Note: Since the unknown is in the numerator, we are easily able to solve, as shown above. If the unknown is in the denominator we can use a method that involves cross product. The cross product is the product of one of the ratios and the denominator of the second ratio.