Understanding Discounts and Percentage Changes

The video tutorial explores two mathematical problems involving percentages. The first problem involves calculating the highest marked price one can afford with a 25% discount, using algebra to solve for the maximum price. The second problem examines the effect of a 25% growth followed by a 25% shrinkage on an initial amount, demonstrating that the final amount is less than the starting value. The tutorial emphasizes understanding percentage calculations and their real-world applications.

If you have $50 and there's a 25% off sale, what is the highest marked price you can afford?

• $75

• $66.67

• $50

• $40

What is the algebraic expression for the sale price if the marked price is x and the discount is 25%?

• x * 0.25

• x / 0.25

• x + 0.25x

• x - 0.25x

How do you calculate the highest marked price you can afford if the sale price is $50?

• Multiply $50 by 0.75

• Subtract $50 from 0.75

• Divide $50 by 0.75

• Add $50 to 0.75

What is the result of dividing $50 by 0.75 in terms of money?

• $75.00

• $66.67

• $33.33

• $50.00

If an amount grows by 25% in the first year, what is the new amount if you start with $100?

• $75

• $150

• $100

• $125

What happens to an amount if it grows by 25% and then shrinks by 25%?

• It remains the same

• It doubles

• It increases

• It decreases

After a 25% growth, what is the percentage of the original amount if it shrinks by 25%?

• 100%

• 93.75%

• 75%

• 125%

What is the final amount after a 25% increase followed by a 25% decrease on $100?

• $75

• $94.75

• $125

• $100

Why does a 25% increase followed by a 25% decrease result in a net loss?

• Because the increase is on a smaller base

• Because the decrease is on a larger base

• Because percentages are additive

• Because of rounding errors

What is the final amount if $125 shrinks by 25%?

• $100

• $93.75

• $125

• $75