A pizza is cut into two pieces in the ratio of 3 : 7 by weight. The bigger of…

To find the final ratio of the three pieces, we need to carefully track how the pizza is divided in stages.

Step-by-Step Analysis
First Division:

The pizza is cut into two pieces in a ratio of 3:7.

This means the two pieces represent 3/10 and 7/10 of the total weight.

Second Division:

The larger piece (7/10) is further cut in a ratio of 4:7.

To find the size of these two new pieces, divide the 7/10 portion into 11 parts (4 + 7 = 11).

First new piece: (4/11) × (7/10) = 28/110.

Second new piece: (7/11) × (7/10) = 49/110.

Calculate Final Ratio:

We now have three pieces with weights: 3/10, 28/110, and 49/110.

To compare them, convert 3/10 to a denominator of 110: (3 × 11) / (10 × 11) = 33/110.

The weights are now 33/110, 28/110, and 49/110.

The final ratio is 33:28:49.