The marching band is holding a fundraiser. The band is selling t-shirts for $22 and yearbooks for $23. 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 amount of money earned from selling t-shirts is 22x.
The total amount of money earned from selling yearbooks is 23y.
The total amount of merchandise sold is x + y.
According to the problem, the goal is to sell at least $2,400 in merchandise:
22x + 23y ≥ 2400
This is a linear inequality in two variables.
To find a solution, we could use trial and error, or we could graph the inequality and shade the region that satisfies it.
One possible solution is:
x = 90 (sell 90 t-shirts)
y = 70 (sell 70 yearbooks)
Check: 22x + 23y = 1980 + 1610 = 3590 > 2400 (OK)
Therefore, one possible solution to this scenario is to sell 90 t-shirts and 70 yearbooks. The total amount of money earned would be:
22(90) + 23(70) = 1980 + 1610 = 3590.
To find a solution to this scenario, we need to determine a combination of t-shirt sales (at $22 each) and yearbook sales (at $23 each) that will result in at least $2,400 in merchandise sales. Let's set up an equation to represent this situation.
Let's assume x represents the number of t-shirts sold and y represents the number of yearbooks sold.
The total amount earned from selling t-shirts is 22x dollars, and the total amount earned from selling yearbooks is 23y dollars.
According to the scenario, the total amount earned from selling t-shirts and yearbooks should be at least $2,400. Therefore, we have the equation:
22x + 23y ≥ 2400
Now, we need to find a combination of values for x and y that satisfy this equation.
To begin, we can look for specific values that satisfy this equation. Start by substituting different possible values for x or y, and find a combination that works.
For example, if we set x = 100 and y = 100, the equation becomes:
22 * 100 + 23 * 100 ≥ 2400
2200 + 2300 ≥ 2400
4500 ≥ 2400
Since 4500 is indeed greater than or equal to 2400, this combination works.
Therefore, the solution is to sell at least 100 t-shirts and 100 yearbooks to meet the minimum target of $2,400 in merchandise sales.