1. **Stating the problem:** Sam's savings and Ali's savings relate as follows: $\frac{3}{5}$ of Sam's savings equals $\frac{1}{4}$ of Ali's savings. Ali saves 56 more than Sam. We need to find: (a) The ratio of Sam's savings to Ali's savings. (b) Their total amount of savings. 2. **Define variables:** Let Sam's savings be $S$ and Ali's savings be $A$. 3. **Write the equation from the problem:** $$\frac{3}{5}S = \frac{1}{4}A$$ 4. **Express $A$ in terms of $S$:** Multiply both sides by 20 (the least common multiple of 5 and 4) to clear denominators: $$20 \times \frac{3}{5}S = 20 \times \frac{1}{4}A$$ $$4 \times 3S = 5A$$ $$12S = 5A$$ Divide both sides by 5: $$\cancel{12}S \times \frac{1}{\cancel{5}} = \cancel{5}A \times \frac{1}{\cancel{5}}$$ $$\frac{12}{5}S = A$$ So, $$A = \frac{12}{5}S$$ 5. **Use the information that Ali saves 56 more than Sam:** $$A = S + 56$$ Substitute $A$ from step 4: $$\frac{12}{5}S = S + 56$$ 6. **Solve for $S$:** Bring all terms to one side: $$\frac{12}{5}S - S = 56$$ Rewrite $S$ as $\frac{5}{5}S$: $$\frac{12}{5}S - \frac{5}{5}S = 56$$ Subtract fractions: $$\frac{12 - 5}{5}S = 56$$ $$\frac{7}{5}S = 56$$ Multiply both sides by $\frac{5}{7}$: $$S = 56 \times \frac{5}{7}$$ Simplify: $$S = 8 \times 5 = 40$$ 7. **Find $A$:** $$A = S + 56 = 40 + 56 = 96$$ 8. **Find the ratio of Sam's savings to Ali's savings:** $$S : A = 40 : 96$$ Simplify by dividing both by 8: $$\cancel{40} : \cancel{96} = 5 : 12$$ 9. **Find their total savings:** $$S + A = 40 + 96 = 136$$ **Final answers:** (a) The ratio of Sam's savings to Ali's savings is $5 : 12$. (b) Their total amount of savings is 136.