Babken bought a bag of peaches at the local market. He gave his sister one third of all the
peaches plus one more. Then he gave two thirds of the remaining peaches to his brother. Babken
kept the last three peaches for himself. How many peaches did Babken buy?
+91 Let x be the number of peaches Babken originally bought.
We can now represent the situation with an equation:
\({\frac {1} {3}}(x-{\frac {1} {3}}x-1)=3\)
The -1/3x and -1 comes from giving 1/3 and one extra to his sister.
The 1/3 at the front of the first bracket comes from the 1/3 he was left with after giving 2/3 to his brother.
Solving:
\({\frac {1} {3}}(x-{\frac {1} {3}}x-1)=3\)
\(x-{\frac {1} {3}}x-1=9\)
\(x-{\frac {1} {3}}x=10\)
\({\frac {2} {3}}x=10\)
\(x=15\)
Therefore Babken originally bought 15 peaches.
