3r+2f < 400
3*45 = 135, so 2f < 265
3*45 = 135, so 2f < 265
Given that Joy paid more than 400 pesos and the total cost of 3 kilos of rice is less than 400 pesos, we can calculate the maximum amount Joy can spend on rice.
Let's assume Joy can spend x pesos on rice.
The cost of 3 kilos of rice is 45 pesos per kilo, so the total cost of rice would be 3 * 45 = 135 pesos.
Since the total cost of rice is less than 400 pesos, we know that x < 135.
To find the maximum amount Joy can pay for 2 kilos of fish, we subtract the maximum amount Joy can spend on rice from the total amount she paid:
400 pesos - x pesos = amount Joy can spend on 2 kilos of fish.
To find the greatest amount to the nearest peso, we need to find the largest possible value for x that satisfies x < 135 and 400 - x > 0.
Since we want to find the maximum possible value for the amount spent on fish, the greatest amount Joy can spend on 2 kilos of fish is when she spends the least amount on rice.
In this case, since the cost of 3 kilos of rice is 135 pesos, Joy can spend the maximum amount on fish:
400 - 135 = 265 pesos.
Therefore, the greatest amount Joy can pay for 2 kilos of fish, to the nearest peso, is 265 pesos.
Let's break down the problem step by step:
1. Determine the cost of 3 kilos of rice:
Since each kilo of rice costs 45 pesos, the total cost of 3 kilos of rice would be: 3 kilos * 45 pesos/kilo = 135 pesos.
2. Set up the inequality for the total cost of rice and fish:
Let's assume the cost of 2 kilos of fish is x pesos. According to the problem, the total amount spent on rice and fish should be less than 400 pesos. Therefore, we can write the following inequality:
135 pesos + x pesos < 400 pesos.
3. Solve the inequality for the greatest amount Joy can pay for 2 kilos of fish:
Subtract 135 pesos from both sides of the inequality:
x pesos < 400 pesos - 135 pesos,
x pesos < 265 pesos.
The greatest amount Joy can pay for 2 kilos of fish is 265 pesos, rounded to the nearest peso.