Problem solving (point of intersection)
You are considering changing your cell phone plan . Company A offered a flat fee of $40 plus 10cents for each additional min of use. Company B offers a monthly flat fee of $20 plus 15 cents for each additional min of use. What plan would you choose?
I came up with this equation, is that the one I want?
Y=.10x+40
Y=.15x+20
I'm stuck at that point
now graph the two lines.
To find out which plan is better for you, you need to find the point of intersection between the two equations. This point represents the number of minutes of usage where both plans cost the same.
To find the point of intersection, you need to set the two equations equal to each other and solve for x.
So, your equations are:
Y = 0.10x + 40
Y = 0.15x + 20
Setting them equal to each other:
0.10x + 40 = 0.15x + 20
Now, we can simplify the equation by subtracting 0.10x from both sides:
40 = 0.05x + 20
Subtracting 20 from both sides:
20 = 0.05x
Now, divide both sides by 0.05:
20 / 0.05 = x
x = 400
So, the point of intersection (x) is 400 minutes of usage. This means that if you use 400 minutes or less, both plans will cost the same.
To determine which plan is better for you, you can substitute this value of x back into either of the original equations. Let's choose the first equation:
Y = 0.10x + 40
Substituting x = 400:
Y = 0.10 * 400 + 40
Y = 40 + 40
Y = 80
So, for 400 minutes of usage or less, both plans will cost you $80.
Now, compare this cost with the cost of the second plan (Company B). If the cost of the second plan for 400 minutes is lower than $80, then Company B's plan would be a better choice for you. If it is higher, then Company A's plan would be better.
You can calculate the cost for the second plan (Company B) using the equation Y = 0.15x + 20 and substituting x = 400:
Y = 0.15 * 400 + 20
Y = 60 + 20
Y = 80
In this case, both plans cost the same for 400 minutes of usage, so you could choose either plan.