Question

The Fountain of Youth health-products store is going out of business. To help clear out their remaining merchandise, they are having a "Save Your Age" sale. Each customer saves the percent equal to his or her age on each purchase. a. Marcus bought a case of all-natural soda originally priced at \(\$ 18 .\) If Marcus is 12 years old, how much did he pay for the case of soda? b. Marcus' father bought some soap and shampoo originally priced at \(\$ 24 .\) If he is 36 years old, how much did he pay for the items? c. Marcus' grandmother is 63 years old. She bought a juicer originally priced at \(\$ 57 .\) How much did she pay?

Short answer

Marcus pays \$15.84\. Marcus' father pays \$15.36\. Marcus' grandmother pays \$21.09\.

Step-by-step solution

Calculate Marcus' discount

Marcus is 12 years old, so he saves 12% on his purchase. To find the discount amount, multiply the original price of the soda, \(\$18\), by 12%, or 0.12: \[ 18 \times 0.12 = 2.16 \]

Subtract the discount from the original price (Marcus)

To find out how much Marcus pays, subtract the discount from the original price: \[ 18 - 2.16 = 15.84 \] Marcus pays \$15.84\ for the case of soda.

Calculate Marcus' father's discount

Marcus' father is 36 years old, so he saves 36% on his purchase. Multiply the original price of the soap and shampoo, \(\$24\), by 36%, or 0.36: \[ 24 \times 0.36 = 8.64 \]

Subtract the discount from the original price (Marcus' father)

Subtract the discount from the original price to find out how much Marcus' father pays: \[ 24 - 8.64 = 15.36 \] Marcus' father pays \$15.36\ for the soap and shampoo.

Calculate Marcus' grandmother's discount

Marcus' grandmother is 63 years old, so she saves 63% on her purchase. Multiply the original price of the juicer, \(\$57\), by 63%, or 0.63: \[ 57 \times 0.63 = 35.91 \]

Subtract the discount from the original price (Marcus' grandmother)

Subtract the discount from the original price to determine how much Marcus' grandmother pays: \[ 57 - 35.91 = 21.09 \] Marcus' grandmother pays \$21.09\ for the juicer.

Key concepts

percentage savings

Understanding how to calculate percentage savings is a valuable skill. When a store offers a discount, this is usually expressed as a percentage. The percentage savings tell you how much less you will pay compared to the original price.
In the example exercise, customers save a percentage of the price equal to their age. Calculating these savings involves multiplying the original price by the percentage (in decimal form). For Marcus, who is 12 years old, his savings calculation for a \$18 case of soda is made by multiplying the price by 0.12 (12% as a decimal):
\[ 18 \times 0.12 = 2.16 \]
This step-by-step method helps clarify the savings.

calculating discounts

To calculate a discount, you follow a straightforward process. First, find the percentage rate of the discount, converting the percentage to a decimal. Then, multiply the original price by this decimal.
For instance, Marcus' father, who is 36 years old, bought soap and shampoo originally priced at \$24. His discount is 36%, converted to 0.36 in decimal form. To find the discount amount, multiply:
\[ 24 \times 0.36 = 8.64 \]
Once you have the discount in dollars, you subtract it from the original price to find how much he actually pays.

subtraction in real-world scenarios

Subtraction is a fundamental math skill used in many real-world scenarios. When dealing with discounts, you often need to subtract the discount amount from the original price to find the final price you need to pay.
For example, Marcus' grandmother purchased a juicer originally priced at \$57. She saved 63%, which is \$35.91. To find out how much she pays:
\[ 57 - 35.91 = 21.09 \]
This formula shows how simple subtraction helps determine the discounted price, making it a practical skill in everyday life.

real-life math applications

Using math in real-life applications makes learning more meaningful. Calculating discounts and savings helps understand how much you spend and save in daily purchases.
The exercise about 'Save Your Age' sale provides an excellent example. Each person's age determined their savings percentage—the higher the age, the higher the discount. Marcus' savings were 12%, his father's were 36%, and his grandmother's were 63%.
This type of problem shows practical uses of math beyond the classroom, from budgeting groceries to understanding sales offers. Learning these skills helps in making more informed financial decisions.