To find out how much health food Sanji needs to buy for the membership cost to equal the shipping charges, we can set up an equation.
Let \( x \) be the total cost of the health food he buys in dollars. Without the membership, he pays 3% shipping on this amount, which can be expressed as \( 0.03x \). With the premium membership costing $45, we need to find when these two costs are equal:
\[ 0.03x = 45 \]
Now we can rearrange this equation to express it in a more standard form:
- Starting with \( 0.03x = 45 \)
- We can multiply both sides by \( \frac{1}{0.03} \) to solve for \( x \):
\[ x = \frac{45}{0.03} \]
This shows that the shipping charges will equal the membership cost when the total cost of the health food purchased is \( x \).
To model this situation, the correct equation from the options given is derived from the equation for the shipping charges:
If we manipulate the equation we started with, we can see that:
\[ 0.03x + 45 = 0 \ 0.03x + 45 = x \]
This is very similar to the provided options.
Among the options given, the equation that potentially represents this is:
- 1.03x = 45
However, it is important to clarify that the first step reveals that the cost of health food should equal the membership cost, leading ultimately to
\[ x = 0.03x + 45 \]
Thus the correct choice from your list that best fits the model of the shipping charges between membership and non-membership is:
- x = 0.03x + 45
This equation signifies that the total cost \( x \) is what you pay for the health food without the membership, equating it to the additional shipping cost plus the membership fee.
1 answer