<em>Question:</em>
<em>Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage. </em>
<em>The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is .
</em>
<em>The solution to the inequality is .
</em>
<em>Sal’s mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.</em>
Answer:
a. ![150 + 51x < 100 + 55x](https://tex.z-dn.net/?f=150%20%2B%2051x%20%3C%20100%20%2B%2055x)
b. ![x > 12.5](https://tex.z-dn.net/?f=x%20%3E%2012.5)
c. At least 13 months
Step-by-step explanation:
Given
First Phone;
![Cost = \$100](https://tex.z-dn.net/?f=Cost%20%3D%20%5C%24100)
<em>(monthly)</em>
Second Phone;
![Cost = \$150](https://tex.z-dn.net/?f=Cost%20%3D%20%5C%24150)
<em />
<em> (monthly)</em>
<em></em>
Solving (a): The inequality
<em></em>
Represent the number of months with x
The first phone is expressed as:
![100 + 55x](https://tex.z-dn.net/?f=100%20%2B%2055x)
The second phone is expressed as:
![150 + 51x](https://tex.z-dn.net/?f=150%20%2B%2051x)
For the second to be less expensive that the first, the inequality is:
![150 + 51x < 100 + 55x](https://tex.z-dn.net/?f=150%20%2B%2051x%20%3C%20100%20%2B%2055x)
Solving (b): Inequality Solution
![150 + 51x < 100 + 55x](https://tex.z-dn.net/?f=150%20%2B%2051x%20%3C%20100%20%2B%2055x)
Collect Like Terms
![51x-55x](https://tex.z-dn.net/?f=51x-55x%3C100%20-%20150)
![-4x](https://tex.z-dn.net/?f=-4x%3C-50)
Solve for x
![x > -50/-4](https://tex.z-dn.net/?f=x%20%3E%20-50%2F-4)
![x > 12.5](https://tex.z-dn.net/?f=x%20%3E%2012.5)
Solving (c): Interpret the solution in (b)
implies 13, 14, 15....
Hence, She'll keep the second phone for a period of at least 13 months