For $46, Joel can rent a machine to make novelty buttons to sell at the county fair. The materials cost $0.39 per button. How many buttons must he sell at $1.40 each in order to make a profit. Identify the graph that shows all the possible answers.
A: 45, 46, 47, 48.......
B: 47, 48 ,49, 50.......
C: 46, 47, 48, 49.......
D: 44, 45 , 46, 47.....
1.40x > 46 + .39x
x > 45.54
any number over 46 will work.
45,46,47,48
To determine the number of buttons Joel must sell to make a profit, we need to consider the costs and revenues involved.
Let's break down the costs and revenues per button:
Cost per button: $0.39
Revenue per button: $1.40
Profit per button: Revenue per button - Cost per button
Profit per button: $1.40 - $0.39
Profit per button: $1.01
To make a profit, Joel needs to sell enough buttons to cover the cost of renting the machine, which is $46.
Number of buttons to sell for break-even: Total cost / Profit per button
Number of buttons to sell for break-even: $46 / $1.01
Number of buttons to sell for break-even: approximately 45.54
Since you cannot sell a fraction of a button, Joel would need to sell at least 46 buttons to cover the costs and make a profit.
Looking at the options provided:
A: 45, 46, 47, 48.......
B: 47, 48 ,49, 50.......
C: 46, 47, 48, 49.......
D: 44, 45 , 46, 47.....
Out of these options, the one that includes at least 46 buttons is option C: 46, 47, 48, 49.......
So, the graph that shows all the possible answers is C: 46, 47, 48, 49.......
To find the number of buttons Joel must sell to make a profit, we need to consider the costs and the revenue.
Let's start by determining the cost per button. The materials cost $0.39 per button. Since Joel can rent the machine for $46, we can assume that the maintenance cost per button is negligible.
Next, let's determine the revenue per button. Joel sells each button for $1.40.
To calculate the profit per button, we subtract the cost per button from the revenue per button:
Profit per button = Revenue per button - Cost per button
Profit per button = $1.40 - $0.39 = $1.01
Now, we need to determine how many buttons Joel needs to sell to cover the $46 renting cost. To find that, we divide the renting cost by the profit per button:
Number of buttons to sell = Renting cost / Profit per button
Number of buttons to sell = $46 / $1.01 ≈ 45.54
Since Joel cannot sell a fraction of a button, he needs to sell at least 46 buttons to cover the costs and make a profit.
Now, let's analyze the answer choices:
A: 45, 46, 47, 48......
B: 47, 48, 49, 50......
C: 46, 47, 48, 49......
D: 44, 45, 46, 47......
From our calculation, we determined that Joel needs to sell at least 46 buttons. The only answer choice that includes 46 as an option is option C: 46, 47, 48, 49......
Therefore, the graph that shows all the possible answers is C: 46, 47, 48, 49......