Ruth baked a big cake to sell during the school fair. She cut the cake into many equal pieces. She sold two- thirds of the pieces. She gave half of the remaining pieces to her friends. She then had 6 pieces left to bring home. Into how many pieces did she cut the cake?
2/3 + (1/2)(1/3) = 5/6
So, 1/6 of the original number is 6
Jdid
To find out how many pieces Ruth cut the cake into, we can work backward from the information given.
Let's denote the total number of pieces Ruth initially had as "x".
According to the information provided:
- Ruth sold two-thirds of the pieces, leaving her with one-third. So, she had (1/3)x pieces remaining.
- She gave half of the remaining pieces to her friends, leaving her with half. So, she had (1/2) * (1/3)x pieces remaining.
- Finally, she had 6 pieces left, which means (1/2) * (1/3)x = 6.
To solve this equation, we can simplify it step by step:
(1/2) * (1/3)x = 6
(1/6)x = 6
x = 6 * 6
x = 36
Therefore, Ruth initially cut the cake into 36 pieces.