1. **Stating the problem:** A transporter uses two lorries, one 7-tonne and one 14-tonne, to transport 133 tonnes of sand. The 7-tonne lorry makes $x$ trips, the 14-tonne lorry makes $y$ trips. The cost per trip is 3000 for the 7-tonne and 4000 for the 14-tonne lorry. Total cost is 47000. We need to write equations, solve for $x$ and $y$, and find the profit if paid 500 per tonne. 2. **Writing the equations:** - Total sand transported: $7x + 14y = 133$ - Total cost: $3000x + 4000y = 47000$ 3. **Using substitution method:** From the first equation, solve for $x$: $$7x + 14y = 133 \implies 7x = 133 - 14y \implies x = \frac{133 - 14y}{7}$$ 4. **Substitute $x$ into the cost equation:** $$3000\left(\frac{133 - 14y}{7}\right) + 4000y = 47000$$ Simplify: $$\frac{3000}{7}(133 - 14y) + 4000y = 47000$$ $$\frac{3000 \times 133}{7} - \frac{3000 \times 14y}{7} + 4000y = 47000$$ $$\frac{399000}{7} - 6000y + 4000y = 47000$$ $$\frac{399000}{7} - 2000y = 47000$$ 5. **Isolate $y$:** $$-2000y = 47000 - \frac{399000}{7}$$ Calculate $\frac{399000}{7} = 57000$: $$-2000y = 47000 - 57000 = -10000$$ Divide both sides by $-2000$: $$y = \frac{-10000}{-2000} = 5$$ 6. **Find $x$ using $y=5$:** $$x = \frac{133 - 14 \times 5}{7} = \frac{133 - 70}{7} = \frac{63}{7} = 9$$ 7. **Calculate profit:** Total sand transported = 133 tonnes. Payment = $500 \times 133 = 66500$ Total cost = 47000 Profit = $66500 - 47000 = 19500$ **Final answers:** - $x = 9$ trips - $y = 5$ trips - Profit = 19500