✏️AGES
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\underline{\mathbb{PROBLEM:}}[/tex]
- 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.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\underline{\mathbb{ANSWER:}}[/tex]
[tex]\qquad\Large\rm» \:\: \green{Lisa \:is\: 17\: years\: old}[/tex]
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\underline{\mathbb{SOLUTION:}}[/tex]
- Represent x and y as the ages of Ana and Lisa respectively. Formulated equations of the given statement.
- [tex]\begin{cases}x + y = 45&\red{(eq.\:1)}\\(x-6) = 2(y-6)&\red{(eq. \:2)}\end{cases} [/tex]
- 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.
- [tex]\begin{cases}x = 45 - y\\(x-6) = 2(y-6)\end{cases} [/tex]
- [tex]\begin{cases}x = 45 - y\\(45 - y-6) = 2(y-6)\end{cases} [/tex]
- [tex]\begin{cases}x = 45 - y\\39 - y =2y - 12\end{cases} [/tex]
- [tex]\begin{cases}x = 45 - y\\39 + 12 =2y + y\end{cases} [/tex]
- [tex]\begin{cases}x = 45 - y\\51 =3y\end{cases} [/tex]
- [tex]\begin{cases}x = 45 - y\\ \begin{gathered} \frac{51}{3} = \frac{ \cancel3y}{ \cancel3} \end{gathered}\end{cases} [/tex]
- [tex]\begin{cases}x = 45 - y\\y = 17\end{cases} [/tex]
[tex]\therefore[/tex] Lisa is 17 years old.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#CarryOnLearning
