Question

In January 2009, the price of rice in Singapore

was $x per kilogram. A food catering company
spent an average of $350 on rice each month.

If the difference in the amount of rice ordered
is 30 kg, formulate an equation in x and show
that it reduces to 20x² + 3x - 35 = 0.

Answer 1

To solve the problem, let's assume the price of rice in January 2009 was $x per kilogram. The food catering company spent $350 on rice each month and bought 30 kg less rice than the previous month. By calculating the difference in expenditure, we can formulate the equation 20x² + 3x - 35 = 0.

Step-by-step explanation:

To solve this problem, let's break it down step by step:

1. Let's assume the price of rice in January 2009 was $x per kilogram.
2. The food catering company spent $350 on rice each month, which means they bought a certain amount of rice at the given price.
3. The difference in the amount of rice ordered is 30 kg, which means the catering company bought 30 kg less rice than the previous month.
4. To formulate the equation, we can calculate the difference in expenditure on rice between the two months.
5. The amount spent in the previous month would be $x (price per kg) multiplied by the amount of rice ordered.
6. The amount spent in the current month would be $x (price per kg) multiplied by the amount of rice ordered minus 30 kg.
7. The difference in expenditure is $350 (current month expenditure) minus $x (previous month expenditure). This gives us an equation: $350 - $x = $x * (amount of rice ordered - 30).
8. Simplifying the equation, we can derive 20x² + 3x - 35 = 0.