Question:
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.
The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is .
The solution to the inequality is .
Sal’s mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.
Answer:
a. [tex]150 + 51x < 100 + 55x[/tex]
b. [tex]x > 12.5[/tex]
c. At least 13 months
Step-by-step explanation:
Given
First Phone;
[tex]Cost = \$100[/tex]
[tex]Additional = \$55[/tex] (monthly)
Second Phone;
[tex]Cost = \$150[/tex]
[tex]Additional = \$51[/tex] (monthly)
Solving (a): The inequality
Represent the number of months with x
The first phone is expressed as:
[tex]100 + 55x[/tex]
The second phone is expressed as:
[tex]150 + 51x[/tex]
For the second to be less expensive that the first, the inequality is:
[tex]150 + 51x < 100 + 55x[/tex]
Solving (b): Inequality Solution
[tex]150 + 51x < 100 + 55x[/tex]
Collect Like Terms
[tex]51x-55x<100 - 150[/tex]
[tex]-4x<-50[/tex]
Solve for x
[tex]x > -50/-4[/tex]
[tex]x > 12.5[/tex]
Solving (c): Interpret the solution in (b)
[tex]x > 12.5[/tex] implies 13, 14, 15....
Hence, She'll keep the second phone for a period of at least 13 months
