question in description

Question

Ricki has a prepaid

cellphone. Last week Ricki

made 4 calls and sent 20 text

messages which cost him $4.

This week he made 10 calls

and sent 5 text messages

which cost him $5.50. Write

a system describing the

number of calls, c, and the

number of text messages, t,

that Ricki made over the past

two weeks.

4c + 20t = 4

10c + 5t = 5.5

Answer 1

To get an equation for both weeks together, you would simply add the equations together.

14c + 25t = 9.5.

Then, if you wanted to solve for c and t, you could do that as well.

using the first equation given you can say c = 1-5t (this is achieved after subtracting the 20 t from both sides and then dividing everything by 4).

Then you can substitute that back into the 2nd equation:

10 (1-5t) + 5t = 5.5

Simplifying:

10 - 50t + 5t = 5.5

10 - 45t = 5.5

4.5 = 45t

t = .1

Substitute this back into the first equation to solve for c.

4c + 20(.10) = 4

4c + 2 = 4.

4c = 2

c = .5

Therefore we can solve this system of equations to determine that calls cost 50 cents and texts cost 10 cents.