Inequality in One Variable Problem (paging service)

[SCSmith]

AirTouch advertises local paging service for $6.95 per month for up to 400 pages, and $.10 per page thereafter. A competitor advertises paging service for $3.95 per month for up to 400 pages and $.15 per page thereafter. For what number of pages per month is the AirTouch plan less expensive?

Let x = number of pages.

. . .6.95(400) + 10x < 3.95(400) + 0.15x

. . .2780 + 0.10x < 1580 + 15x

. . .1200 < 0.5x

. . .2400 < x

 

[Denis]

What grade are you in, Smitty?

 

[skeeter]

AirTouch advertises local paging service for $6.95 per month for up to 400 pages, and $.10 per page thereafter. A competitor advertises paging service for $3.95 per month for up to 400 pages and $.15 per page thereafter. For what number of pages per month is the AirTouch plan less expensive?

airtouch charges ... 6.95 + .10x, where x is the number of pages beyond 400

competitor ... 3.95 + .15x, same definition for x

6.95 + .10x < 3.95 + .15x

695 + 10x < 395 + 15x

300 < 5x

60 < x

airtouch will be less expensive for x > 60 pages ... that means > 460 pages total.