Question

A farmer is budgeting for planting soybeans and wheat. Planting soybeans costs $200 per acre, and planting wheat costs $500 per acre. If he wants to spend no more than $100,000 on both crops, which inequality describes the situation using 's' for soybeans and 'w' for wheat? a) 200s + 500w ≤ 100,000 b) 200s + 500w ≥ 100,000 c) 200s - 500w ≤ 100,000 d) 200s - 500w ≥ 100,000

Answer 1

The correct inequality for the farmer's budget situation is 200s + 500w ≤ 100,000, where 's' is soybeans acres and 'w' is wheat acres.

Step-by-step explanation:

The inequality that describes the situation where a farmer is budgeting for planting soybeans and wheat, with soybeans costing $200 per acre and wheat costing $500 per acre, and the farmer wanting to spend no more than $100,000 on both crops is represented by option a) 200s + 500w ≤ 100,000. Here, 's' represents the number of acres of soybeans, and 'w' represents the number of acres of wheat. To not exceed the budget, the total cost of planting both crops must be less than or equal to $100,000.

Answer 2

The inequality that represents this situation is 200s + 500w ≤ 100,000 .

So, the correct answer is a) 200s + 500w ≤ 100,000.

To solve this problem, we need to formulate an inequality that represents the farmer's budget constraints for planting soybeans and wheat. Let's use 's' to represent the number of acres of soybeans and 'w' to represent the number of acres of wheat.

Given:

1. Planting soybeans costs $200 per acre.

2. Planting wheat costs $500 per acre.

3. The farmer wants to spend no more than $100,000 on both crops.

We need to create an inequality that reflects the total cost of planting both crops being less than or equal to $100,000.

Step 1: Write down the cost per acre for each crop.

- The cost for planting soybeans per acre is $200. So, for 's' acres, it will be 200s .

- The cost for planting wheat per acre is $500. So, for 'w' acres, it will be 500w .

Step 2: Add the costs for both crops.

- The total cost for planting both crops is 200s + 500w

Step 3: Apply the budget constraint.

- The farmer does not want to spend more than $100,000. So, the total cost of planting both crops must be less than or equal to $100,000.

Step 4: Formulate the inequality.

- The inequality that represents this situation is 200s + 500w ≤ 100,000 .

So, the correct answer is a) 200s + 500w ≤ 100,000.

This inequality indicates that the total cost of planting soybeans and wheat, at the given rates per acre, should not exceed $100,000.