Sanji buys a lot of health food from a company that charges 3% on each item for shipping. If he purchased a premium membership for $45 a year, the shipping would be free. He wants to know how much food he would have to buy each year so that the cost of the membership would be the same as the cost of the shipping charges without the membership. What equation does this situation model?(1 point)

Question

Responses

Answer 1

To find the equation that models the situation described, we need to set up the relationship between the total cost of shipping without the membership and the cost of the membership.

Let \( x \) be the total amount (in dollars) of food Sanji buys in a year.

1. The membership costs $45 annually.
2. The shipping cost without the membership is 3% of the total purchase amount, which can be expressed as \( 0.03x \).

We want to find out when the cost of the membership is equal to the cost of shipping:

\[ 0.03x = 45 \]

This equation states that the total shipping cost \( 0.03x \) for the food purchased equals the yearly membership fee of $45. Thus, the equation modeling this situation is:

\[ 0.03x = 45 \]