Question

Matthew has 5/9 much money as Nancy. Nacy has thrice that of Pearlyn. Matthew has $286 more than Pearlyn. How much money do they have altogether?

59. ​Matthew has $\frac{5}{9}$ as much money as Nancy. Nancy has thrice that of Pearlyn. Matthew has $286 more than Pearlyn. How much money do they have altogether?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{money}\mathrm{Pearlyn}\mathrm{has}=\mathrm{Rs}\mathrm{x} \\ \mathrm{Money}\mathrm{with}\mathrm{Mathew}=\mathrm{Rs}\left(\mathrm{x}+286\right) \\ \mathrm{Money}\mathrm{with}\mathrm{Nancy}=\mathrm{Rs}3\mathrm{x} \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ \mathrm{Mathew}\text{'}\mathrm{s}\mathrm{money}=\frac{5}{9}\times \mathrm{Money}\mathrm{with}\mathrm{Nancy} \\ \mathrm{x}+286=\frac{5}{9}\times \left(3\mathrm{x}\right) \\ \mathrm{x}+286=\frac{5\mathrm{x}}{3} \\ 3\mathrm{x}+858=5\mathrm{x} \\ 858=2\mathrm{x} \\ \mathrm{x}=429 \\ \mathrm{Let}\mathrm{the}\mathrm{money}\mathrm{Pearlyn}\mathrm{has}=\mathrm{Rs}\mathrm{x}=\mathrm{Rs}429 \\ \mathrm{Money}\mathrm{with}\mathrm{Mathew}=\mathrm{Rs}\left(\mathrm{x}+286\right)=\mathrm{Rs}\left(429+286\right)=\mathrm{Rs}715 \\ \mathrm{Money}\mathrm{with}\mathrm{Nancy}=\mathrm{Rs}3\mathrm{x}=\mathrm{Rs}\left(3\times 429\right)=\mathrm{Rs}1287 \\ \mathrm{Total}\mathrm{money}\mathrm{with}\mathrm{all}=429+715+1287=\mathrm{Rs}2431 \end{gathered}$$
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