Solve multistep percent problems · lesson

Tax, tips, markups, and commission

💡 Find the percent of the amount; add it on if the question asks for the total.

Tax, tips, markups, and commission are all a percent of some amount.

First find the percent: change it to a decimal and multiply.

Then read the question. Does it want just that part, or the new total? For a total, add the part to the start amount.

🧠 Let's work it out

A $30 meal has 7% tax. What is the total?

What do you think comes next?

💡 A sale price is the percent you still pay, and two discounts in a row are applied one after the other.

If something is 25% off, you pay 100% − 25% = 75% of the price.

Two discounts in a row do not just add. The second one is taken from the new, lower price.

🧠 Let's work it out

A $90 coat is 25% off, then another 20% off the sale price. What is the final price?

What do you think comes next?

💡 Percent change is the change divided by the original amount, times 100.

First find how much it changed. Subtract the smaller from the larger.

Then divide the change by the original amount, the one you started with. Multiply by 100 to get a percent.

To grow by a percent, find that percent of the start and add it on.

🧠 Let's work it out

A price goes from $50 to $65. What is the percent increase?

Change = 65 − 50 = 15.
Divide by the original: 15 ÷ 50 = 0.3.
Change to a percent: 0.3 × 100 = 30, a 30% increase.
Another example: a drop from 120 to 96 is 24 ÷ 120 = 0.2, a 20 percent decrease.

What do you think comes next?

original: the amount you started with
percent change: how much something changed, as a percent of where it started

💡 Simple interest is principal times rate times years.

When you save money, the bank may pay you interest. Simple interest is the same amount every year.

Find one year's interest: the rate times the money. Then multiply by the number of years.

🧠 Let's work it out

You save $800 at 4% simple interest for 3 years. How much interest do you earn?

What do you think comes next?

💡 If you know the price after a change, divide by the percent you paid to find the original.

Sometimes you know the sale price and need the price before the sale.

Find what percent of the original you paid. Then divide the sale price by that decimal.

🧠 Let's work it out

After 25% off, a game costs $54. What was the original price?

What do you think comes next?