the sum of ana's and liza's age is 45 .six years ago ana's was twice as old as l...

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francescaramos377 @francescaramos377

September 2022 1 8 Report

the sum of ana's and liza's age is 45 .six years ago ana's was twice as old as liza's then. how old is lisa?

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$\underline{\mathbb{PROBLEM:}}$

The sum of Ana and Lisa's age is 45. Six years ago Ana was twice as old as Liza. Then, how old is Lisa.

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$\underline{\mathbb{ANSWER:}}$

$\qquad\Large\rm» \:\: \green{Lisa \:is\: 17\: years\: old}$

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$\underline{\mathbb{SOLUTION:}}$

- Represent x and y as the ages of Ana and Lisa respectively. Formulated equations of the given statement.

$\begin{cases}x + y = 45&\red{(eq.\:1)}\\(x-6) = 2(y-6)&\red{(eq. \:2)}\end{cases}$

- Find the solution of x from the first equation in terms of y then substitute it to the second equation which is the age of Lisa.

$\begin{cases}x = 45 - y\\(x-6) = 2(y-6)\end{cases}$

$\begin{cases}x = 45 - y\\(45 - y-6) = 2(y-6)\end{cases}$

$\begin{cases}x = 45 - y\\39 - y =2y - 12\end{cases}$

$\begin{cases}x = 45 - y\\39 + 12 =2y + y\end{cases}$

$\begin{cases}x = 45 - y\\51 =3y\end{cases}$

$\begin{cases}x = 45 - y\\ \begin{gathered} \frac{51}{3} = \frac{ \cancel3y}{ \cancel3} \end{gathered}\end{cases}$

$\begin{cases}x = 45 - y\\y = 17\end{cases}$

$\therefore$ Lisa is 17 years old.

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