Maria paid 80 cents each for some packages of cards. She sold all but 18 packages for $2 each, making a profit of $48. How many packages of cards did she buy?
How do I set this problem up to solve it?
profit = revenue - cost, so
2(x-18) - 0.80x = 48
x = 70
X = number of packages
Maria paid 0.80/pkg so total cost = 0.80X
She sold all but 18 so she sold X-18 packages for 2.00 each so she sold X-18 for 2.00 each. Her income was 2.00(.80-x). Her cost was 0.8X. Her profit was 48.00.
2.00(X-18) - 0.80X = 48.00
Solve for X
To set up this problem, we can break it down into a few steps:
Step 1: Determine the cost per package.
Maria paid 80 cents (or $0.80) for each package of cards.
Step 2: Calculate the sell price of packages.
Maria sold all but 18 packages for $2 each. This means she sold (total number of packages - 18) packages for $2 each.
Step 3: Calculate the profit made.
The profit she made can be calculated as the sell price - the cost price for each package. In this case, the profit is $48.
Step 4: Create an equation.
Using the information from steps 1, 2, and 3, we can create an equation to solve for the total number of packages:
[Cost per package (80 cents) * (Total number of packages - 18)] = Profit ($48)
Step 5: Solve the equation.
By rearranging the equation and solving for the total number of packages, we can find the answer.
Let's calculate the answer:
0.80 * (Total number of packages - 18) = 48
Now, we just need to solve this equation to find the total number of packages.