Question

Solve the following problem in two different ways.

3 [ n + 1/4 ] = 17.25
Explain why both strategies work to solve for n.

Answer 1

To solve the equation 3[n + 1/4] = 17.25, you can use two different strategies: distributing and isolating n, or using the floor function and inequalities to find the range of possible values for n. Both strategies work because they follow the rules of algebra.

Step-by-step explanation:

To solve the equation 3[n + 1/4] = 17.25, we can use two different strategies.

Strategy 1:

1. Distribute 3 to the terms inside the bracket: 3n + 3/4 = 17.25
2. Subtract 3/4 from both sides of the equation: 3n = 17.25 - 3/4 = 16.5
3. Divide both sides of the equation by 3: n = 16.5/3 = 5.5

Strategy 2:

1. Divide both sides of the equation by 3: [n + 1/4] = 17.25/3 = 5.75
2. Since [n + 1/4] means the greatest integer less than or equal to n + 1/4, we know that n + 1/4 must be between 5.75 and 6.
3. Therefore, n must be between 5.75 - 1/4 = 5.5 and 6 - 1/4 = 5.75.

Both strategies work to solve for n because they follow the rules of algebra and lead to the same solution.