To grow his ranch, a rancher is purchasing some bulls, which cost $5,300 apiece, and some cows, which cost $890 apiece. He doesn't want to spend more than $20,000 at this time.

Question

Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of bulls
y = the number of cows

Answer 1

To represent the situation where a rancher is purchasing bulls and cows without exceeding a budget of $20,000, we can use the following variables:

• Let \( x \) be the number of bulls.
• Let \( y \) be the number of cows.

Each bull costs $5,300, so the total cost for bulls is \( 5300x \).

Each cow costs $890, so the total cost for cows is \( 890y \).

The total cost should not exceed $20,000. Thus, we can express this as the inequality:

\[ 5300x + 890y \leq 20000 \]

To write this inequality in standard form, we can rearrange it to have all terms on one side:

\[ 5300x + 890y - 20000 \leq 0 \]

This is the inequality in standard form that represents the given situation.