Question

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 membership would be the same as the cost of the shipping charges without the membership. What equation models this situation

Answer 1

To find the amount of food Sanji needs to buy each year so that the cost of membership equals the cost of shipping without the membership, we can set up an equation.

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

1. The cost of shipping without the membership is 3% of the total amount of food purchased. This can be expressed as: \[ \text{Shipping cost} = 0.03x \]

2. The cost of the membership is $45 per year.

To find the point at which these costs are equal, we set up the equation: \[ 0.03x = 45 \]

This equation models the situation where the cost of the shipping charges without membership equals the cost of the premium membership.

To solve for \( x \): \[ x = \frac{45}{0.03} \] \[ x = 1500 \]

Sanji would need to buy $1500 worth of food in a year for the cost of the membership to be equivalent to the shipping charges he would incur without it.