Question

6.
number of video games | income (dollars) | production cost (dollars) | profit (dollars)
--- | --- | --- | ---
x | 35x | 10x + 1500 | 25x - 1500
0 | | |
25 | | |
50 | | |
60 | | |
200 | | |
300 | | |
the productions cost, and the income are equivalent when there are
select...
video
games produced.

Explanation:

Step1: Calculate Income for each x

For $x=0$: $35(0) = 0$
For $x=25$: $35(25) = 875$
For $x=50$: $35(50) = 1750$
For $x=60$: $35(60) = 2100$
For $x=200$: $35(200) = 7000$
For $x=300$: $35(300) = 10500$

Step2: Calculate Production Cost for each x

For $x=0$: $10(0)+1500 = 1500$
For $x=25$: $10(25)+1500 = 250+1500=1750$
For $x=50$: $10(50)+1500 = 500+1500=2000$
For $x=60$: $10(60)+1500 = 600+1500=2100$
For $x=200$: $10(200)+1500 = 2000+1500=3500$
For $x=300$: $10(300)+1500 = 3000+1500=4500$

Step3: Calculate Profit for each x

For $x=0$: $25(0)-1500 = -1500$
For $x=25$: $25(25)-1500 = 625-1500=-875$
For $x=50$: $25(50)-1500 = 1250-1500=-250$
For $x=60$: $25(60)-1500 = 1500-1500=0$
For $x=200$: $25(200)-1500 = 5000-1500=3500$
For $x=300$: $25(300)-1500 = 7500-1500=6000$

Step4: Find x where Income = Cost

Set $35x = 10x + 1500$
$35x - 10x = 1500$
$25x = 1500$
$x = \frac{1500}{25} = 60$

Answer:

Completed Table:

Number of Video Games	Income (dollars)	Production Cost (dollars)	Profit (dollars)
25	875	1750	-875
50	1750	2000	-250
60	2100	2100	0
200	7000	3500	3500
300	10500	4500	6000

Break-Even Point:

Production cost and income are equivalent when there are 60 video games produced.