Answer:
To find out how much free space Nereo and Azeneth will have when they first have the same amount of space left, we start by setting up equations to represent the free space remaining on each phone over time.
Let t be the number of seconds that have elapsed since they started recording.
**Nereo's phone:**
- Starts with 1,000 MB of free space.
- Uses 7 MB of space per second.
The free space on Nereo's phone after t seconds is given by:
1000 - 7t
**Azeneth's phone:**
- Starts with 1,255 MB of free space.
- Uses 10 MB of space per second.
The free space on Azeneth's phone after t seconds is given by:
1255 - 10t
We want to find the time t when they have the same amount of free space left. Therefore, we set the two expressions equal to each other:
1000 - 7t = 1255 - 10t
To solve for t , first isolate t by simplifying and rearranging the equation:
1000 - 7t = 1255 - 10t
Add 10t to both sides to start eliminating t from one side:
1000 + 3t = 1255
Subtract 1000 from both sides to further isolate t :
3t = 255
Finally, solve for t by dividing both sides by 3:
t = 255/3 = 85
Now that we have \( t = 85 \), we can find the amount of free space left on both phones at that time by substituting \( t \) back into either equation.
Using Nereo's equation:
1000 - 7(85) = 1000 - 595 = 405
Using Azeneth's equation to confirm:
1255 - 10(85) = 1255 - 850 = 405
Both phones will have 405 MB of free space left after 85 seconds. Therefore, when they first have the same amount of space left, the amount of free space will be:
405
Step-by-step explanation: