If a pack of 12 pencils is sold for $4.80, how many pencils can you buy for $2.00?
$\frac{4.8}{12}=\frac{2}{x}$
To find the number of pencils that can be purchased for a specific amount of money when given a price for a bulk pack, we can use the concept of unit price. We are given that a pack of 12 pencils costs \$4.80. We need to determine how many pencils, denoted by @@MATH_TOKEN_5@@, can be bought for \$2.00. We assume the price per pencil remains constant.
The relationship between the price and the quantity is directly proportional, which is expressed by the equation provided: \[\frac{4.8}{12} = \frac{2}{x}\] The left side of the equation represents the cost of a single pencil in dollars, while the right side represents the same cost ratio for a smaller quantity and price. To find the cost of one pencil, we perform the division: \[\frac{4.8}{12} = 0.4\] So, each pencil costs \$0.40.
Now that we know the unit price of one pencil is \$0.40, we can determine how many pencils can be bought for \$2.00 by dividing the total budget by the unit price. The equation becomes: \[0.4 = \frac{2}{x}\] Multiplying both sides by \(x\) and then dividing by 0.4, we get: \[x = \frac{2}{0.4} = 5\] Therefore, for \$2.00, one can buy 5 pencils.
Understanding unit prices is essential in everyday shopping. For example, when you are in a supermarket, you often see the price per unit (e.g., price per gram or price per item) on the shelf labels. By knowing the unit price, you can easily determine how much of a product you can afford with your available budget or compare which package size offers better value. This same proportional reasoning applies to many areas, such as fuel efficiency (distance per liter) or hourly wages (income per hour).