At the supermarket, a certain item has increased from 75 cent per pound to 81 cent per bag. What is the percent increase in the cost of the item?
%C= vf-vi/vi ×100%
%C = 81-75/75×100%
%C = 8%
Percentage increase: (81-75)/75*100=8%
To find the percent increase in the cost of the item, we need to calculate the difference between the new and old prices, and then divide that difference by the old price. Finally, we multiply the result by 100 to get the percentage.
Let's calculate the percent increase step-by-step:
Step 1: Find the difference between the new and old prices:
New price - Old price = 81 cents per bag - 75 cents per pound
Step 2: Convert the old price to the same unit as the new price:
Since the old price is given in pounds and the new price is given in bags, we need to convert one unit to the other. Let's say 1 bag is equal to x pounds.
1 bag = x pounds
Step 3: Use the given values to find the conversion factor:
To convert bags to pounds, we can set up a proportion using the given information:
1 bag / x pounds = 81 cents / 75 cents
Cross-multiplying gives us:
75 cents * 1 bag = x pounds * 81 cents
75 cents = 81x cents
Now divide both sides by 81 cents:
75 cents / 81 cents = 81x cents / 81 cents
0.9259 = x
Therefore, 1 bag is approximately equal to 0.9259 pounds.
Step 4: Calculate the difference between the new and old prices in the same unit:
New price - Old price = 81 cents per bag - (75 cents per pound * 0.9259 pounds per bag)
Simplifying this calculation:
81 cents per bag - (75 cents per pound * 0.9259 pounds per bag)
= 81 cents per bag - 69.4383 cents per bag
≈ 11.5617 cents per bag
Step 5: Calculate the percent increase in the cost of the item:
Percent increase = (Difference / Old price) * 100
Percent increase = (11.5617 cents per bag / 75 cents per pound) * 100
≈ 15.42%
Therefore, the percent increase in the cost of the item is approximately 15.42%.
To find the percent increase in the cost of the item, follow these steps:
1. Determine the initial cost: In this case, the initial cost is 75 cents per pound.
2. Determine the final cost: In this case, the final cost is 81 cents per bag.
3. Calculate the difference between the final cost and the initial cost: 81 cents - 75 cents = 6 cents.
4. Calculate the percent increase by dividing the difference by the initial cost and multiplying by 100: (6 cents / 75 cents) × 100 = 8%.
Therefore, the percent increase in the cost of the item is 8%.