Skill: Compare two valid strategies

To compare two valid strategies, first solve the problem in two different ways. Then explain:

1. What each strategy represents.
2. Why both methods match the situation.
3. Why they give the same answer.
4. Which method is more efficient or easier to use.

Example: A jacket costs 48$. It is on sale for$25%$off. Then$$6$ is added for shipping. What is the total cost?

Strategy 1: Find the discount first

A $25\%$ discount means subtract $25\%$ of the original price.

Convert $25\%$ to a decimal:

$$25\% = 0.25$$

Find the discount:

$$0.25 \times 48 = 12$$

The discount is 12$. Subtract it from the original price:

$$48 - 12 = 36$$

Now add the shipping cost:

$$36 + 6 = 42$$

The total cost is:

$$\boxed{\$42}$$

This strategy represents the amount being taken away from the original price.

Strategy 2: Find the percent that remains

If $25\%$ is taken off, then $100\% - 25\% = 75\%$ remains.

Convert $75\%$ to a decimal:

$$75\% = 0.75$$

Find $75\%$ of the original price:

$$0.75 \times 48 = 36$$

Then add the shipping cost:

$$36 + 6 = 42$$

The total cost is:

$$\boxed{\$42}$$

This strategy represents the part of the price that remains after the discount.

Compare the strategies

Both strategies are valid because:

• Strategy 1 finds the discount and subtracts it.
• Strategy 2 finds the remaining price directly.
• Both find the same sale price, 36$, and the same total,$$42$.

Strategy 2 is a little more efficient because it uses one multiplication instead of finding the discount and then subtracting. However, Strategy 1 may be more transparent when you want to know exactly how much money was saved.

When comparing strategies, look for whether each operation represents the quantities in the problem—not just whether the final answers happen to match.