Problem Solving

swerve wrote:The price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge. A 10-minute call costs $2.90 and a 16-minute call costs $4.40. How much does a 13-minute call cost?

A. $3.55
B. $3.57
C. $3.58
D. $3.65
E. $3.77

The OA is D

Source: Manhattan Prep

Let C = price of connection fee
Let M = the price PER MINUTE

A 10-minute call costs $2.90
We can write: C + 10M = 2.90

A 16-minute call costs $4.40.
We can write: C + 16M = 4.40

How much does a 13-minute call cost?
So far, we have:
C + 10M = 2.90
C + 16M = 4.40

ONE (slower) approach would be to solve the system for C and M, and then calculate the cost of a 13-minute call.
The FASTER approach is to recognize that something great happens when we ADD the two equations

We get: 2C + 26M = 7.30
Now divide both sides by 2 to get: C + 13M = 3.65

Since C + 13M represents the TOTAL cost of a 13-minute call, we can conclude that a 13-minute call costs $3.65

Answer: D

Cheers,
Brent

BTW, you posted the same question in January: https://www.beatthegmat.com/the-price-o ... 05974.html

Cheers,
Brent