Question

How do you solve \[\dfrac{z}{{z + 15}} = \dfrac{4}{9}\]?
a). 13
b). 19
c). 12
d). 14

Answer 1

Hint: We solve this in two ways that are by substituting each option in the given problem and if the LHS is equal to RHS, then the substituted option is the correct one. But we don’t do it by this method. We solve this using the transposition method. That is grouping the variable term on one side and the constant term on another side.

Complete step-by-step solution:
Given, \[\dfrac{z}{{z + 15}} = \dfrac{4}{9}\].
Now to simplify we cross multiply it.
\[z \times 9 = 4 \times \left( {z + 15} \right)\]
\[\Rightarrow 9z = 4z + 60\]
We transpose \[4z\] which is present in the right-hand side of the equation to the left-hand side of the equation by subtracting \[4z\]on the left-hand side of the equation.
\[9z - 4z = 60\]
\[\Rightarrow 5z = 60\]
We transpose or shift 5 to the RHS by dividing 5 on the right hand side of the equation.
\[z = \dfrac{{60}}{5}\]
\[ \Rightarrow z = 12\].
Hence, option (c) is correct.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘z’ in the given problem. If LHS is equal to RHS then our obtained answer is correct.
\[\dfrac{z}{{z + 15}} = \dfrac{4}{9}\]
\[\dfrac{{12}}{{12 + 15}} = \dfrac{4}{9}\]
\[\dfrac{{12}}{{27}} = \dfrac{4}{9}\]
\[ \Rightarrow \dfrac{4}{9} = \dfrac{4}{9}\]
Hence the obtained answer is correct.
In the above, we did the transpose of addition and subtraction. Similarly, if we have multiplication, we use division to transpose. If we have division, we use multiplication to transpose. Follow the same procedure for these kinds of problems.