Question

A mobile company charges a fixed rate of x cents per minute for the first 120 minutes of talk time and another rate of y cents per minute for each additional minute of talk time. Ethan paid $26.80 and $32.40 for 175 mins and 210 minutes of talk time on two different occasions respectively. find the amount he has to pay if he uses 140 mins of talk time.

Answer 1

$21.2

Explanation:

From the problem given, we express them as algebra so that we can easily solve;

the total charge on a call greater than 120min is given as;

120x + y(n - 120) = total cost of call

where n is the number of minutes which is greater than 120;

• Ethan paid $26.80 for 175 mins

n = 175min here;

120x + y(175 - 120) = 26.80

120x + 55y = 26.80 ----- (I)

• $32.40 for 210 minutes

n = 210min

120x + y(210 - 120) = 32.4

120x + 90y = 32.4 ----- (II)

Now let us solve both equations for y and x;

120x + 55y = 26.80 ----- (I)

120x + 90y = 32.4 ----- (II)

subtract the two equations;

90y - 55y = 32.4 - 26.8

35y = 5.6

y =
`(5.6)/(35)` = 0.16cents

then x;

120x = 26.8 - 55y from equation I

120x = 26.8 - 55(0.16)

120x = 18

x =
`(18)/(120)` = 0.15cents

Find the cost of 140min of talk time;

n =140min;

= 120(0.15) + 0.16(140 - 120)

= 18 + 0.16(20)

= 18 + 3.2

= $21.2