Problem 54 - Algebra A Combined Function

Question

A gasoline station decreased the price of a \(\$ 0.95\) cola by \(15 \%\). Find the decrease in price and the new price.

Step-by-Step Solution

Answer

The decrease in price is $0.1425 and the new price is $0.8075.

Step 1: Calculate the Amount of Decrease

A decrease of 15% means you want to find 15% of 0.95. To do this, convert 15% to a decimal by dividing by 100, which gives 0.15. Then, multiply 0.15 by 0.95 to find the amount of decrease. \[0.15 \times 0.95 = 0.1425\] So, the price decreased by $0.1425.

Step 2: Calculate the New Price

Subtract the amount of decrease from the original price to find the new price. The original price is \(0.95, and the decrease is \)0.1425.\[0.95 - 0.1425 = 0.8075\]Thus, the new price for the cola is $0.8075.

Key Concepts

Decimal Conversion

When dealing with percentages, it's essential to understand how to convert them into decimals. It makes calculations much simpler. To convert a percentage to a decimal, follow these simple steps:

• Divide the percentage by 100. This changes the percentage into a decimal value you can use for further calculations.

For instance, if you have 15%, converting it to a decimal involves dividing by 100:\[ 15\% = \frac{15}{100} = 0.15 \]Now, you've turned 15% into 0.15, which represents the same value in decimal form. This decimal conversion is crucial, especially when calculating the percentage of a number in exercises like the one shown.

Multiplication

Once the percentage has been converted to a decimal, you can start calculating what part of the original value it represents. This is done through multiplication.To find out how much of an item’s price is reduced by a certain percentage, multiply the original price by the decimal value of the percentage. For our cola example:

• The price of the cola is originally \(0.95.
• The decimal for 15% is 0.15.
• Therefore, multiply \)0.95 by 0.15.

This multiplication gives the actual decrease in cost: \[ 0.95 \times 0.15 = 0.1425 \]Thus, the price is lowered by $0.1425. Multiplication helps us find how much less the cola costs due to the price drop.

Price Calculation

Price calculation involves determining the new price after accounting for any changes, like a discount. Once the decrease amount is known, the next step is calculating the new sale price.Here's how you can achieve this:

• You start with the original price of the item. In this case, that's \(0.95 for the cola.
• Subtract the decrease in price you've previously calculated.

With our example, subtract \)0.1425 from \(0.95:\[ 0.95 - 0.1425 = 0.8075 \]The new price equals \)0.8075. This calculation results in the final sales price after considering the discount. It's essential for adjusting the selling cost of items.

Subtraction

Subtraction comes into play when you are trying to find out what remains after removing a certain amount from a whole. After finding out how much money is reduced from the original price, it’s crucial to perform subtraction to figure out the final price.To subtract successfully:

• Identify the original full price and the amount to be subtracted.
• Confirm the decrease amount properly, as calculated from the multiplication step.
• Finally, subtract the decrease from the original price.

In our specific example, you subtract the decrease of \(0.1425 from the original price of \)0.95:\[ 0.95 - 0.1425 = 0.8075 \]Subtraction ensures that you get the accurate remaining balance, which in this case tells us the cola's new price after the discount.