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The sum of two numbers is 41. The first number is 7 more than the second. What is the first number?

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UK2019viz

✏️NUMBERS

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Problem: The sum of two numbers is 41. The first number is 7 more than the second. What is the first number?

Solution: Represent x and y as the first and second number respectively. Make equations of the given statement.

  • [tex] \begin{cases}x = y + 7& \green{(eq. \: 1)} \\ x + y = 41 & \green{(eq. \: 2)}\end{cases}[/tex]

- Substitute x from the first equation to the second equation in terms of y.

  • [tex] \begin{cases}x = y + 7 \\ (y + 7) + y = 41\end{cases}[/tex]

  • [tex] \begin{cases}x = y + 7 \\ y + 7 + y = 41\end{cases}[/tex]

  • [tex] \begin{cases}x = y + 7 \\ 2y + 7 = 41\end{cases}[/tex]

  • [tex] \begin{cases}x = y + 7 \\ 2y = 41 - 7\end{cases}[/tex]

  • [tex] \begin{cases}x = y + 7 \\ 2y = 34\end{cases}[/tex]

  • [tex] \begin{cases}x = y + 7 \\ \begin{gathered} \frac{ \cancel2y}{ \cancel2} = \frac{34}{2} \end{gathered}\end{cases}[/tex]

  • [tex] \begin{cases}x = y + 7 \\ y = 17\end{cases}[/tex]

- Substitute y to the first equation to find the x also known as the first number.

  • [tex] \begin{cases}x = 17 + 7 \\ y = 17\end{cases}[/tex]

  • [tex] \begin{cases}x = 24 \\ y = 17\end{cases}[/tex]

- Therefore, the first number is:

  • [tex] \large \rm First \: Number = \boxed{ \rm \green{ \: 24 \: }}[/tex]

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[tex] \large\underline{\mathbb{PROBLEM}:} [/tex]

  • The sum of two numbers is 41. The first number is 7 more than the second. What is the first number?

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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \Large \rm{The \: first \: no. \: is \: 24} [/tex]

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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

» Let x and y be the first and the second number respectively. Create two equations by the given statements.

  • [tex] \begin{cases} x + y = 41 \\ x = y + 7 \end{cases} \quad \begin{align} \tt{(eq. \: 1)} \\ \tt{(eq. \: 2)} \end{align} [/tex]

» Find y in the first equation then substitute it to the second equation in terms of x and to find the first number.

  • [tex] \begin{cases} y = 41 - x \\ x = y + 7 \end{cases} [/tex]

  • [tex] \begin{cases} y = 41 - x \\ x = 41 - x + 7 \end{cases} [/tex]

  • [tex] \begin{cases} y = 41 - x \\ x + x = 41 + 7 \end{cases} [/tex]

  • [tex] \begin{cases} y = 41 - x \\ 2x = 48 \end{cases} [/tex]

  • [tex] \begin{cases} y = 41 - x \\ 2x/2 = 48/2 \end{cases} [/tex]

  • [tex] \begin{cases} y = 41 - x \\ x = 24 \end{cases} [/tex]

[tex] \therefore [/tex] The first number is 24.

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