Juan is comparing the cell phone plans shown in the advertisement. Plan A charges a $15 monthly fee plus $0.40 per min. Plan B charges a $30 monthly fee plus $0.25 per min. For what number of minutes of use do the plans cost the same? How much will that be?
15 + .40m = 30 + .25m
Calculate m. Once you find m, insert its value on either side to answer the last question.
Do the arithmetic.
I'll be glad to check your answer.
Well, Juan must be quite the bargain hunter! Let's figure out when both plans cost the same. We'll start by setting up an equation.
For Plan A, the total cost is given by $15 + $0.40m, where m is the number of minutes used.
For Plan B, the total cost is $30 + $0.25m.
To find when the plans cost the same, we'll set these two expressions equal to each other:
$15 + $0.40m = $30 + $0.25m.
Now, let's do some math to find the value of m.
Subtracting $15 from both sides, we get:
$0.40m - $0.25m = $30 - $15.
Combining like terms, we have:
$0.15m = $15.
Dividing both sides by $0.15, we get:
m = $15 / $0.15 = 100.
So, when Juan uses 100 minutes, both plans will cost the same.
And how much will that be? Well, let's substitute m = 100 back into either expression for total cost.
For example, using Plan A, the total cost would be:
$15 + $0.40 × 100 = $15 + $40 = $55.
So, when Juan uses 100 minutes, the cost for both plans will be $55. That's a whole lot of clown noses!
To find the number of minutes for which the plans cost the same, we can set up an equation and solve for the variable. Let's assume x represents the number of minutes of use.
For Plan A, the total cost (C) can be calculated using the formula:
C = 15 + 0.40x
For Plan B, the total cost (C) can be calculated using the formula:
C = 30 + 0.25x
We want to find the value of x for which Plan A's cost equals Plan B's cost. So we can set up the equation:
15 + 0.40x = 30 + 0.25x
To solve this equation, we can start by subtracting 15 from both sides:
0.40x = 15 + 0.25x - 15
Simplifying further, we get:
0.40x - 0.25x = 15
Combining like terms:
0.15x = 15
To isolate x, we can divide both sides by 0.15:
x = 15 / 0.15
Simplifying further:
x = 100
Therefore, the plans cost the same for 100 minutes of use.
To find the cost for that number of minutes, we can substitute x = 100 into either of the formulas. Let's use Plan A's formula:
C = 15 + 0.40x
C = 15 + (0.40 * 100)
C = 15 + 40
C = 55
So, for 100 minutes of use, the cost for both plans would be $55.