Respuesta :
• You know that the sum of the two numbers must be:
[tex]5.678[/tex]In order to find any pair of numbers whose sum is that number shown above, you can subtract 1 from it:
[tex]5.678-1=4.678[/tex]Now you can set up that:
[tex]1+4.678=5.678[/tex]• To find any pair of numbers whose difference is:
[tex]9.876[/tex]You can add 2 to it:
[tex]9.876+2=11.876[/tex]Then, you can set up that:
[tex]11.876-2=9.876[/tex]• Let be "x" and "y" the numbers that add up to 5.678. and whose difference is 9.876.
Then, you can set up these equations:
[tex]\begin{gathered} x+y=5.678\text{ (Equation 1)} \\ \\ x-y=9.876\text{ (Equation 2)} \end{gathered}[/tex]• To solve the riddle, you can follow these steps:
- Set up a System of equations using the equations found in the previous part:
[tex]\begin{gathered} \begin{cases}x+y=5.678 \\ \\ x-y=9.876\text{ }\end{cases} \\ \end{gathered}[/tex]- Apply the Elimination Method by adding both equations and solving for "x":
[tex]\begin{gathered} \begin{cases}x+y=5.678 \\ \\ x-y=9.876\text{ }\end{cases} \\ ------------ \\ 2x=15.554 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{15.554}{2} \\ \\ x=7.777 \end{gathered}[/tex]- Substitute the value of "x" into one of the original equations and solve for "y":
[tex]\begin{gathered} (7.777)+y=5.678 \\ \\ y=5.678-7.777 \\ \\ y=-2.099 \end{gathered}[/tex]Therefore, the answers are:
• Any pair of numbers whose sum is 5.678:
[tex]1\text{ and }4.678[/tex]• Any pair of numbers whose difference is 9.876:
[tex]11.876\text{ and }2[/tex]• Equations that represents the riddle:
[tex]\begin{gathered} x+y=5.678\text{ (Equation 1)} \\ \\ x-y=9.876\text{ (Equation 2)} \end{gathered}[/tex]• Solution of the riddle:
[tex]\begin{gathered} x=7.777 \\ y=-2.099 \end{gathered}[/tex]
