Final answer:
The cost for Plan A can be expressed as 55 + 3x, where x is the number of premium channels selected. The cost for Plan B can be expressed as 25 + 8y, where y is the number of premium channels selected. The two plans will cost the same when the number of premium channels selected is 3.75 + 0.375x.
Step-by-step explanation:
To write an expression for the cost of Plan A, we can start with the base cost of $55 and add $3 for each premium channel selected. So, if x is the number of premium channels, the cost of Plan A can be expressed as 55 + 3x. For Plan B, the base cost is $25 and an additional $8 is added for each premium channel selected. So, if y is the number of premium channels, the cost of Plan B can be expressed as 25 + 8y. To find the point at which the two plans cost the same, we can set the expressions for Plan A and Plan B equal to each other and solve for the number of premium channels, x and y.
55 + 3x = 25 + 8y
Subtracting 25 from both sides:
30 + 3x = 8y
Dividing both sides by 8:
3.75 + 0.375x = y
This means that when the number of premium channels selected is equal to 3.75 + 0.375x, the cost for Plan A and Plan B will be the same.