Question

In this activity, you will write expressions and equations to represent a real-world situation and draw a conclusion about the situation based on the solution to your equation.

The expression for the number of tiles Bruce used can be written as x. The expression for the number of tiles Felicia used can also be written as x.

Bruce: y = 5x + 2

Felicia: y = 5x + 5

Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.

Answer 1

The contradiction in the simplified equation (2 is not equal to 5) indicates that there is no solution for x. Thus, Bruce and Felicia cannot have used the same number of tiles; their expressions ensure different tile counts.

To determine whether Bruce and Felicia used the same number of tiles, we can set their expressions for the number of tiles equal to each other and solve for x.

The expressions for Bruce and Felicia are given by:

Bruce: y = 5x + 2

Felicia: y = 5x + 5

Setting them equal to each other:

5x + 2 = 5x + 5

Now, we can simplify the equation:

Subtracting 5x from both sides:

2 = 5

This leads to a contradiction (2 is not equal to 5). The inconsistent result implies that there is no value of x that satisfies the equation.

Therefore, it is not possible for Bruce and Felicia to have used the same number of tiles based on the given expressions. The equations describe situations where the number of tiles used by Bruce and Felicia will always be different.