James 6

James and Lisa shared some sweets. James took 2/7 of the sweets, and Lisa took the rest. If James took 18 fewer sweets than Lisa, how many sweets did they have altogether at first?

Final Answer:

n =  42

Step-by-step explanation:

$$\begin{gathered} J=2/7\cdot n \\ L=n-J=n-2/7\cdot n=5/7\cdot n \\ J=L-18 \\ \frac{2}{7}\cdot n=\frac{5}{7}\cdot n-18 \\ 2/7\cdot n=5/7\cdot n-18 \\ 3n=126 \\ n=\frac{126}{3}=42 \\ n=42 \\ \text{ Verifying Solution: } \\ J=\frac{2}{7}\cdot n=\frac{2}{7}\cdot 42=\frac{2\cdot 42}{7}=\frac{84}{7}=12 \\ L=n-J=42-12=30 \\ d=L-J=30-12=18 \end{gathered}$$

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