Final answer:
Katie's situation does match the equation for determining the equal cost of ice cream with toppings at two different shops. By setting up an equation and solving for x, the number of toppings needed for equal cost, we find that 4.5 toppings are required, but customers would likely need to order 4 or 5 whole toppings.
Step-by-step explanation:
To determine if Katie's situation matches the equation and to find out how many toppings are required for the ice cream cost to be the same at both shops, we can set up an equation where the total cost is the same for both scenarios. Let x represent the number of toppings. The cost at the first shop would be 3.00 + 0.75x dollars, and the cost at the second shop would be 5.25 + 0.25x dollars. To find the number of toppings where both costs are equal, we can solve the following equation:
3.00 + 0.75x = 5.25 + 0.25x
Now we need to isolate x. Subract 0.25x from both sides:
3.00 + 0.50x = 5.25
Then subtract 3.00 from both sides:
0.50x = 2.25
Finally, divide both sides by 0.50:
x = 4.50
So, a customer would need to order 4.5 toppings for the ice cream to cost the same at either shop. However, since customers typically cannot order half a topping, we'd assume the customer would need to order either 4 or 5 toppings, depending on the shops' policies on fractional toppings. The situation Katie wrote does seem to match the equation, as it is a question of equalizing two linear expressions which represent the cost of ice cream with toppings.