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If you divide a number into 3 equal groups and then divide each group in half, you end up with 13. What number did your start with?

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[tex] \large \bold{\blue{PROBLEM:}} [/tex] If you divide a number into 3 equal groups and then divide each group in half, you end up with 13. What number did your start with?

[tex] \large \bold{\blue{SOLUTION:}} [/tex] Refer 'n' as the number you started. Translate it, make it divide into 3 and divided again into 2 to get 13.

  • [tex] n \div 3 \div 2 = 13 [/tex]

  • [tex] n \cdot \frac{1}{3} \cdot \frac{1}{2} = 13 \\ [/tex]

  • [tex] n \cdot \frac{1}{6} = 13 \\ [/tex]

  • [tex] n \cdot \frac{1}{\cancel6} \cdot \cancel6 = 13 \cdot 6 \\ [/tex]

  • [tex] n = 78 [/tex]

» Checking: If you divide 78 into three, you'll get 26. Half of 26 is 13.

[tex] \large \therefore \underline{\boxed{\tt \purple{The \: number \: is \: 78}}} [/tex]

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