Find the solutions to the mathematical problems.
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A farm made £352 in revenue from sales over the weekend. The revenue came from selling 20 baskets of apples at £12 each and an unknown number of jars of honey at £8 each. Additionally, a worker spent 14 hours (r) maintaining the farm at an hourly rate of £10. Use the following equation to calculate how many jars of honey (h) were sold: Profit = 12a + 8h – 10r.
Use the equation to determine the total revenue from honey sales.
Use the equation to calculate the farm's profit.
Two carpenters make custom furniture and made a total of £1008 in revenue from two products: chairs and tables. The carpenters sold 18 chairs at £20 each and an unknown number of tables at £72 each. They spit the revenue fairly between themselves. Additionally, each carpenter worked for 21 hours (h), and each hour of work added £8 to the total cost of labour. Use the following equation to determine how many tables (t) were sold: Profit = (20c + 72t) ÷ 2 – 8h.
Use the equation to calculate the total revenue from tables.
Use the equation to calculate carpenters' individual profit.
A farmer sold fresh produce at the market and earned £630 in total revenue. The sales included 30 baskets of vegetables at £15 each and an unknown number of crates of fruits at £45 each. Additionally, the farmer paid £120 in market fees (e) and spent 18 hours (h) transporting the goods, where each hour costs £10. Use the following equation to determine how many crates of fruits (f) were sold: Profit = (15v + 45f) – e – 10h.
Use the equation to calculate the total revenue from fruit sales.
Use the equation to determine the farmer's profit.
A car rental service made £1,200 in total revenue over the weekend. The service rented out 15 cars at £50 each and an unknown number of motorbikes at £30 each. Additionally, the company spent £200 on maintenance and paid an employee for 10 hours (h) at £12 per hour. Use the following equation to determine how many motorbikes (m) were rented: Profit = (50c + 30m) – (200 + 12h) – t.
Use the equation to calculate the total revenue from motorbike rentals.
Before the profit can be paid out, the company must pay 30% (or 3/10) in taxes (t). Use the equation to compute the company's profit.
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