Question

Gina has $15$ dollars more than twice as much money as her sister Maria. If Gina gives Maria $30$ dollars, then Gina will have half as much money as her sister. How many dollars does Gina have?

Answer 1

Step-1: Expression for Gina and Maria in both cases:

Let Gina have$\$G$ and Maria have $\$M$

Given that Gina has $15$ dollars more than twice as much money as her sister Maria

$\therefore G=15+2M...\left(i\right)$

Gina gives Maria $30$ dollars, then Gina will have half as much money as her sister
$$\begin{gathered} \therefore G-30=\frac{1}{2}(M+30) \\ \Rightarrow 2G=M+90...\left(ii\right) \end{gathered}$$

Step-2: Solving both the equation to find how many dollars does Gina Have:

$$\begin{gathered} \Rightarrow 2(15+2M)=M+90\mathbf{}\mathbf{[}\mathbf{\because }\mathit{G}\mathbf{=}\mathbf{15}\mathbf{+}\mathbf{2}\mathit{M}\mathbf{]} \\ \Rightarrow 30+4M=M+90 \\ \Rightarrow 4M-M=90-30 \\ \Rightarrow M=\frac{60}{3} \\ =\$20 \end{gathered}$$
Gina have $=15+2\times 20$
$=\$55$

Hence, Gina have $\$55$.