Discussion
A pizza is cut into two pieces in the ratio of 3 :7 by weight. The bigger of the two pieces is further cut in the ratio of 4:7 by weight. Find the ratio of each of the three pieces.
Answer: B
The ratio of the three pieces is 33 : 28 : 49.
Take the whole pizza as 10 parts: the pieces are 3 and 7. The bigger piece, 7, is cut in the ratio 4 : 7, that is into 4/11 and 7/11 of itself.
\[ \begin{aligned} 7 \times \tfrac{4}{11} &= \tfrac{28}{11}, \quad 7 \times \tfrac{7}{11} = \tfrac{49}{11} \\ 3 &= \tfrac{33}{11} \end{aligned} \]
Multiplying all three by 11 gives 33 : 28 : 49 (total 110, which checks with 3 : 7 since 33 : 77). The other ratios do not keep the first cut at 3 : 7.
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