Final answer:
The equation in standard form for the situation described is 5x + y = 20
Step-by-step explanation:
To write an equation that represents the given situation in standard form, we can follow these steps:
1. Assign variables: Let's assign the variable x to represent the number of days the boat is rented, and y to represent the number of days the scuba gear is rented.
2. Calculate costs: Given that the boat rental costs $250 per day and the gear rental costs $50 per day, we can determine the total costs for each:
- - Total boat cost: $250 * x
- - Total gear cost: $50 * y
3. Write the equation: The total amount spent is given as $1000. To represent this in an equation, we can add the two costs and set it equal to the total spent:
- - Total boat cost + Total gear cost = Total spent
- - $250x + $50y = $1000
4. Simplify into standard form: To write the equation in standard form, we want the coefficients (A and B) to be integers with no common factors other than 1, and the constant term (C) to be an integer. In this case, our equation is already in the necessary format. However, if we notice that all terms are divisible by 50, we can divide the entire equation by 50 to simplify it:
- - ($250/50)x + ($50/50)y = ($1000/50)
- - 5x + y = 20
In summary, the equation 5x + y = 20 represents the situation in standard form. The coefficients 5 and 1 represent the costs per day of the boat and gear respectively, while the variables x and y represent the number of days each is rented. The constant term 20 represents the total cost spent.