The marching band is holding a fundraiser. The band is selling t-shirts for $20 and yearbooks for $24. The goal is to sell at least $2,400 in merchandise. Which of the following is a solution to this scenario
There are multiple solutions to this scenario, but one possible solution is:
- Let x be the number of t-shirts sold.
- Let y be the number of yearbooks sold.
- The total revenue generated can be expressed as 20x + 24y.
- The goal is to sell at least $2,400, so we have the inequality 20x + 24y ≥ 2400.
- We want to maximize the revenue, so we want to find the values of x and y that satisfy the inequality and make 20x + 24y as large as possible.
- One way to do this is to use linear programming or graphing techniques, but for simplicity we can try a few values for x and y and see which ones work. Starting with x = 0 and y = 100 (selling 100 yearbooks only), we get 24y = 2400, which satisfies the inequality. However, the revenue is only 24(100) = $2,400, which is the minimum target. We want to do better.
- Let's try increasing the number of t-shirts sold while keeping the number of yearbooks sold the same. If we sell x = 50 t-shirts and y = 100 yearbooks, we get 20x + 24y = 20(50) + 24(100) = $3,000, which is higher than the target. This is a viable solution.
- We could also try selling more t-shirts and fewer yearbooks. For example, if we sell x = 120 t-shirts and y = 50 yearbooks, we get 20x + 24y = 20(120) + 24(50) = $3,240, which is higher than the target. This is another viable solution.
- In fact, there are many other combinations of x and y that would work, such as x = 60 and y = 90, x = 80 and y = 75, x = 100 and y = 62, etc. The key is to find values of x and y that satisfy the inequality and maximize the revenue.
- Therefore, one possible solution to the scenario is to sell 50 t-shirts and 100 yearbooks, or to sell 120 t-shirts and 50 yearbooks (or any other combination that meets the target and maximizes the revenue).
To find a solution to this scenario, we need to determine how many t-shirts and yearbooks need to be sold to reach the goal of selling at least $2,400 in merchandise.
Let's assume the number of t-shirts sold is x and the number of yearbooks sold is y.
According to the given information, the price of each t-shirt is $20 and the price of each yearbook is $24.
The total amount earned from selling t-shirts can be calculated as 20x, and the total amount earned from selling yearbooks can be calculated as 24y.
We know that the total amount earned from selling merchandise should be at least $2,400. This gives us the equation:
20x + 24y ≥ 2400
Now, let's find a possible solution to this equation. We need to find whole number values for x and y that satisfy the inequality.
One possible solution is:
- x = 100, y = 80
If we sell 100 t-shirts and 80 yearbooks, the total amount earned would be:
20 * 100 + 24 * 80 = 2000 + 1920 = $3920
Since $3920 is greater than $2400, this solution satisfies the given condition.
Therefore, the solution to this scenario is to sell 100 t-shirts and 80 yearbooks.