1. **State the problem:** Calculate the value of the expression $60\left(\frac{2}{5} + \frac{7}{12}\right)$. 2. **Formula and rules:** To add fractions, find a common denominator, then add the numerators. 3. **Find common denominator for $\frac{2}{5}$ and $\frac{7}{12}$:** The least common denominator (LCD) of 5 and 12 is 60. 4. **Convert fractions:** $$\frac{2}{5} = \frac{2 \times 12}{5 \times 12} = \frac{24}{60}$$ $$\frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}$$ 5. **Add the fractions:** $$\frac{24}{60} + \frac{35}{60} = \frac{24 + 35}{60} = \frac{59}{60}$$ 6. **Multiply by 60:** $$60 \times \frac{59}{60} = \cancel{60} \times \frac{59}{\cancel{60}} = 59$$ 7. **Final answer:** $$\boxed{59}$$