Problem 11
Question
A gallon jug of brand name nonfat milk costs \(\$ 2.39\). A gallon jug of store brand nonfat milk costs \(\$ 1.99\). Find the savings in a year from buying the store brand if a family buys 3 gallons of nonfat milk per week (52 weeks \(=1\) year).
Step-by-Step Solution
Verified Answer
The annual savings from buying the store brand nonfat milk is \$ 62.40\.
1Step 1: Identify the cost difference per gallon
Subtract the cost of the store brand nonfat milk from the brand name nonfat milk to find the difference in cost per gallon. \( 2.39 - 1.99 = 0.40 \)
2Step 2: Calculate weekly savings
Multiply the cost difference per gallon by the number of gallons purchased per week. \( 0.40 \text{ dollars/gallon} \times 3 \text{ gallons/week} = 1.20 \text{ dollars/week} \)
3Step 3: Calculate annual savings
Multiply the weekly savings by the number of weeks in a year to find the total savings. \( 1.20 \text{ dollars/week} \times 52 \text{ weeks} = 62.40 \text{ dollars/year} \)
Key Concepts
annual savingsunit price comparisonweekly savings
annual savings
Annual savings represent the amount of money you can save over a year by making a certain financial decision. In our exercise, the goal is to determine the yearly savings from choosing a store brand nonfat milk over a brand name milk. By buying a more cost-effective option regularly, you save money each week, and these weekly savings add up over the year.
To calculate annual savings, start by determining how much you save in a week. Then, multiply that amount by the number of weeks in a year (52 weeks). This will give you your total annual savings. In this exercise, the saving per week is \$1.20. By multiplying this amount by 52 weeks, we get the annual savings:
\[1.20 \text{ dollars/week} \times 52 \text{ weeks/year} = 62.40 \text{ dollars/year}\]
Understanding annual savings helps in budgeting and making smarter purchasing decisions.
To calculate annual savings, start by determining how much you save in a week. Then, multiply that amount by the number of weeks in a year (52 weeks). This will give you your total annual savings. In this exercise, the saving per week is \$1.20. By multiplying this amount by 52 weeks, we get the annual savings:
\[1.20 \text{ dollars/week} \times 52 \text{ weeks/year} = 62.40 \text{ dollars/year}\]
Understanding annual savings helps in budgeting and making smarter purchasing decisions.
unit price comparison
Unit price comparison is a method to determine which product offers a better deal by comparing the cost per unit of different options. It is especially useful when the products come in different sizes, brands, or packaging.
In this exercise, the unit price is the cost per gallon of milk. We need to compare the price of the brand name nonfat milk (\$2.39) with the store brand nonfat milk (\$1.99). By subtracting the store brand price from the brand name price:\[2.39 - 1.99 = 0.40 \text{ dollars/gallon},\]
we find the cost difference per gallon. This means the store brand milk is \$0.40 cheaper per gallon. Comparing unit prices is useful in many shopping scenarios to choose the most economical option.
In this exercise, the unit price is the cost per gallon of milk. We need to compare the price of the brand name nonfat milk (\$2.39) with the store brand nonfat milk (\$1.99). By subtracting the store brand price from the brand name price:\[2.39 - 1.99 = 0.40 \text{ dollars/gallon},\]
we find the cost difference per gallon. This means the store brand milk is \$0.40 cheaper per gallon. Comparing unit prices is useful in many shopping scenarios to choose the most economical option.
weekly savings
Weekly savings refer to how much money you can save in a week by switching to a less expensive option. To calculate weekly savings, multiply the price difference per unit by the number of units bought each week.
In this exercise, a family buys 3 gallons of nonfat milk every week. The saving per gallon is \$0.40, so the weekly savings are calculated as follows:\[0.40 \text{ dollars/gallon} \times 3 \text{ gallons/week} = 1.20 \text{ dollars/week}\]
Recognizing weekly savings helps in understanding the immediate benefits of more economy-minded choices. Adding up these small amounts over time can show how much these decisions can positively affect the family's overall budget.
In this exercise, a family buys 3 gallons of nonfat milk every week. The saving per gallon is \$0.40, so the weekly savings are calculated as follows:\[0.40 \text{ dollars/gallon} \times 3 \text{ gallons/week} = 1.20 \text{ dollars/week}\]
Recognizing weekly savings helps in understanding the immediate benefits of more economy-minded choices. Adding up these small amounts over time can show how much these decisions can positively affect the family's overall budget.