Telephone company A charges $3.00 for the first minute of any long distance call and $0.50 for each additional minute. Telephone company B charges $2.00 for the first minute of any long distance call and $0.70 for each additional minute. If the cost of a call lasting x minutes, where x is a positive integer, is $15.00 more with telephone company B than with telephone company A, then what is the value of x?
costA= 3.00 + .5(x-1)
costB = 2.00 + .7(x-1)
2 + .7(x-1) - 3 - .5(x-1) = 15
.7x - .5x - .7 + .5 -1 = 15
.2x = 16.2
x = 81
check:
if x = 81
costA = 3+.5(80) = 43
costB = 2 + .7(80) = 58 , which is $15 more
what is the reason for multiplying the additional minute cost by (x-1) why not just X?
Let's assume that Company A charges $3.00 for the first minute and $0.50 for each additional minute, and Company B charges $2.00 for the first minute and $0.70 for each additional minute.
Let's first consider the cost of a call lasting x minutes with Company A. Since the first minute costs $3.00, and each additional minute costs $0.50, the total cost of the call with Company A is:
Cost with Company A = $3.00 + ($0.50 * (x - 1))
Now, let's consider the cost of the same call lasting x minutes with Company B. Since the first minute costs $2.00, and each additional minute costs $0.70, the total cost of the call with Company B is:
Cost with Company B = $2.00 + ($0.70 * (x - 1))
Given that the cost of the call with Company B is $15.00 more than with Company A, we can set up the following equation:
Cost with Company B - Cost with Company A = $15.00
Substituting the expressions for the costs from above, we have:
($2.00 + $0.70 * (x - 1)) - ($3.00 + $0.50 * (x - 1)) = $15.00
Simplifying the equation, we get:
$2.00 + $0.70 * x - $0.70 + $3.00 - $0.50 * x + $0.50 = $15.00
$0.2 * x + $0.8 = $15.00
$0.2 * x = $14.20
x = $14.20 / $0.2
x = 71
Therefore, x = 71.
To solve this problem, let's analyze the charges of both telephone companies.
For telephone company A:
- First minute costs $3.00.
- Each additional minute costs $0.50.
For telephone company B:
- First minute costs $2.00.
- Each additional minute costs $0.70.
We need to find the value of x, which represents the number of minutes.
Let's set up an equation to represent the cost of the call with each company:
Cost with company A: $3.00 + $0.50 * (x - 1)
Cost with company B: $2.00 + $0.70 * (x - 1)
According to the problem, the cost with company B is $15.00 more than with company A:
Cost with company B - Cost with company A = $15.00
Let's substitute the expressions for the costs:
($2.00 + $0.70 * (x - 1)) - ($3.00 + $0.50 * (x - 1)) = $15.00
Now we can simplify and solve the equation to find the value of x:
$2.00 + $0.70x - $0.70 - $3.00 - $0.50x + $0.50 = $15.00
Combining like terms:
-$1.00 + $0.20x = $15.00
Now isolate the variable:
$0.20x = $15.00 + $1.00
$0.20x = $16.00
Divide both sides by $0.20:
x = $16.00 / $0.20
x = 80
Therefore, the value of x, representing the number of minutes, is 80.