✒️NUMBERS
[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
[tex] \large\underline{\mathbb{PROBLEM}:} [/tex]
- The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers.
[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
[tex] \large\underline{\mathbb{ANSWER}:} [/tex]
[tex] \qquad \LARGE \:\:\rm{71 \:and \: 19} [/tex]
[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]
» Let x and y be the larger and the smaller number respectively. Create two equations by the given statements.
- [tex] \begin{cases} x + y = 90 \\ x = 3y + 14 \end{cases} \quad \begin{align} \tt{(eq. \: 1)} \\ \tt{(eq. \: 2)} \end{align} [/tex]
» Find x in the first equation then substitute it to the second equation in terms of y.
- [tex] \begin{cases} x = 90 - y \\ x = 3y + 14 \end{cases} [/tex]
- [tex] \begin{cases} x = 90 - y \\ 90 - y = 3y + 14 \end{cases} [/tex]
- [tex] \begin{cases} x = 90 - y \\ 3y + y = 90 - 14 \end{cases} [/tex]
- [tex] \begin{cases} x = 90 - y \\ 4y = 76 \end{cases} [/tex]
- [tex] \begin{cases} x = 90 - y \\ 4y/4 = 76/4 \end{cases} [/tex]
- [tex] \begin{cases} x = 90 - y \\ y = 19 \end{cases} [/tex]
» Thus, the smaller number is 19. Find the larger by substituting y to the first equation.
- [tex] \begin{cases} x = 90 - 19 \\ y = 19 \end{cases} [/tex]
- [tex] \begin{cases} x = 71 \\ y = 19 \end{cases} [/tex]
[tex] \therefore [/tex] The larger number is 71 and the smaller number is 19.
[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
(ノ^_^)ノ
