Question

The ratio of \[a\] to \[b\] is \[\dfrac{4}{7}\]. It \[a\] is \[16\], how do you find the value of \[b\]?

Answer 1

Hint: We need to convert the variable \[a\& b\] from ratio form to fraction form. We need to make an equation with the help of given data. After that, we would substitute the known values in the equation. Next, we need to use cross multiplication to find the unknown value in the equation to solve the given problem.

Complete step-by-step solution:
In this question, we have to find the value \[b\] with the help of given data. Here they give the ratio between \[a\] to \[b\] is \[\dfrac{4}{7}\]. This is can also be written as,
\[\dfrac{a}{b} = \dfrac{4}{7} \to equation\left( 1 \right)\] (Here the keyword ratio indicates the division process)
They also give, the value of\[a\]is\[16\]. So, it can be written as,
\[a = 16\]
By substituting these values in the equation\[\left( 1 \right)\], we get
\[equation\left( 1 \right) \to \dfrac{a}{b} = \dfrac{4}{7}\]
\[\dfrac{{16}}{b} = \dfrac{4}{7} \to equation\left( 2 \right)\]
We know that,
\[\dfrac{a}{b} = \dfrac{c}{d} \Rightarrow ad = bc\](This equation explains the operation of cross multiplication)
By using the above formula in the equation\[\left( 2 \right)\], we get
\[equation\left( 2 \right) \to \dfrac{{16}}{b} = \dfrac{4}{7}\]
\[16 \times 7 = 4 \times b\](Here\[a = 16,b = b,c = 4,d = 7\])
So, we get
\[112 = 4b\]
When we move the term\[4\]from the right-hand side to the left-hand side of the above equation we get,
\[\dfrac{{112}}{4} = b\]
By solving the above equation, we get
\[28 = b\]
So, the final answer is,
\[b = 28\]

Note: This question describes the arithmetic operations like addition/ subtraction/ multiplication/ division. Note that when we move the denominator from LHS to RHS or RHS to LHS, it converts into a numerator. When we move the numerator from LHS to RHS or RHS to LHS, it converts into a denominator. This process is involved in the process of cross multiplication. Note that the keyword Ratio indicates the process of division.