Question

the sum of the weigth of a mother, a baby and a dog is 170 pounds . the mother is 100 pounds more than both the baby and the dog combined. If the dog is 60% less than the baby's weight, find the weight of the baby??

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{sum}\mathrm{of}\mathrm{weights}\mathrm{of}\mathrm{baby}\mathrm{and}\mathrm{dog}=\mathrm{x}\mathrm{pounds} \\ \mathrm{Let}\mathrm{the}\mathrm{weight}\mathrm{of}\mathrm{mother}=\mathrm{y}\mathrm{pounds} \\ \mathrm{Now},\mathrm{x}+\mathrm{y}=170.....\left(1\right) \\ -\mathrm{x}+\mathrm{y}=100......\left(2\right) \\ \mathrm{Adding}\left(1\right)\mathrm{and}\left(2\right),\mathrm{we}\mathrm{get} \\ 2\mathrm{y}=270 \\ \Rightarrow \mathrm{y}=\frac{270}{2}=135 \\ \mathrm{Put}\mathrm{y}=135\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ \mathrm{x}+135=170 \\ \Rightarrow \mathrm{x}=35 \\ \mathrm{So},\mathrm{Let}\mathrm{the}\mathrm{weight}\mathrm{of}\mathrm{baby}=\mathrm{z}\mathrm{pounds} \\ \mathrm{weight}\mathrm{of}\mathrm{dog}=\mathrm{z}-60\%\mathrm{of}\mathrm{z}=\mathrm{z}-\frac{3\mathrm{z}}{5}=\frac{2\mathrm{z}}{5} \\ \mathrm{Now},\mathrm{z}+\frac{2\mathrm{z}}{5}=35 \\ \Rightarrow \frac{7\mathrm{z}}{5}=35 \\ \Rightarrow \mathrm{z}=25 \\ \mathrm{So},\mathrm{weight}\mathrm{of}\mathrm{baby}=25\mathrm{pounds} \\ \mathrm{weight}\mathrm{of}\mathrm{dog}=10\mathrm{pounds} \\ \mathrm{Weight}\mathrm{of}\mathrm{mother}=135\mathrm{pounds} \end{gathered}$$