problem solving: using systems?

Question

An overseas phone call is charged at one rate (a fixed amount) for the first minute and at a different rate for each additional minute. If a 7 minute call cost $10 and a 4 min call cost $6.40, find each rate.

Answer 1

Let the rate for first minute be $x and for each subsequent minute be $y
according to the problem,
x+6y=10.......(eqn 1),and
x+3y=6.40.....)eqn 2)
subtracting (2) from(1)
3y=3.60
y=3.60/3=1.20 Plugging y in eqn 1,we get
x+6*1.20=10
x+7.20=10
x=10-7.20=2.80
therefore the charge for the first minute is $2.80 and the same for each subsequent minute is $1.20

Answer 2

Let F = be the fixed amount and R = the rate per minute.
Let x = number of minutes
Total Cost = F + R(x - 1)
NOTE: We only multiply R by x - 1, since the first minute is already charged with fixed amount F.

a 7 minute call cost $10:
The equation is 10 = F + 6R

4 min call cost $6.40
The equation is 6.4 = F + 3R

We have the system:
10 = F + 6R
6.4 = F + 3R

Subtracting the second equation from the first, we get
3.6 = 3R
R = 1.2

Substituting R = 1.2 into the first equation (actually, either of the equations will do), we have
10 = F + 6(1.2)
10 = F + 7.2
F = 2.8

Therefore, the fixed amount for the first minute is $2.80 and the rate per succeeding minute is $1.20.

Answer 3

let fixed rate be F
let second rate be R

thus
10 = (1)F + (7-1)R
10 = F +6R
and
6.40 = (1)F + (4-1)R
6.40 = F + 3R

subtracting the second equation from the first one we get
3.60 = 3R
1.20 = R
and
6.40 = F + 3(1.20)
6.40 = F + 3.60
F = 2.80
verifying
2.80 + 6(1.20) = ?
2.80 + 7.20 = 10 which is correct

so the fixed rate is $2.80 for the first minute and $1.20 for each minute after

Answer 4

The first call at rates r1 and r2 cost
r1 + 6r2 = 10 and the 2'nd cost
r1 + 3r2 = 6.40 so
r1 = $2.80/min and
r2 = $1.20/min

Doug

Answer 5

let M be rate for first minute
A be rate for additional after the first

7 minutes means M + 6A = 10
4 minutes means M + 3A = 6.40, subtract
----------------------
3A = 3.60 so
A = 1.20 $ for each additional minute after the first, and

M = 10 - 6A (from the first equation above)
= 2.80 $ first minute