Federico needs to frost 36 cupcakes for a party. He has already frosted 23 cupcakes and wants to know how many more he has to frost. He writes the following two equations to represent the problem, but does not know which equation is correct:
23 + c = 36
36 - c = 23
Which equation should Federico use? Explain why
Explain how you know which operation to use when solving an equation, give an example
Frederico can use either equation. Do you see why?
I wanted 36 cupcakes but wasted most of my money in my sock collection. So now I’II just have a fourth of that.
Federico should use the equation 36 - c = 23 to represent the problem.
To understand why, let's break down the equation and the problem at hand. Federico already frosted 23 cupcakes, and he needs to frost a total of 36 cupcakes. The equation 23 + c = 36 suggests that Federico is adding the number of cupcakes he has already frosted (23) to the number of cupcakes he needs to frost (c) to get the total number of cupcakes (36). However, this equation is incorrect for the given situation because Federico wants to know how many more cupcakes he has to frost, not the total number of cupcakes.
On the other hand, the equation 36 - c = 23 represents the correct scenario. Here, Federico is subtracting the number of cupcakes he has already frosted (c) from the total number of cupcakes (36) to find out how many more cupcakes he has to frost (23). This equation aligns perfectly with the problem's requirement.
When solving an equation, it's important to pay attention to the context and purpose of the problem. In this case, since Federico wants to know how many more cupcakes he has to frost, subtracting the number already frosted from the total number of cupcakes is the right operation to use.
Let's take another example for clarity. Imagine you have 10 apples, and you want to know how many more apples you need to have a total of 15 apples. In this case, you would use the equation 15 - x = 10, where x represents the number of apples you have. By subtracting the number of apples you have (x) from the total number of apples you want (15), you can find out how many more apples you need to reach your desired total (10).