Question

The charge for sending a telegram is constant for the first 10 or less words and an amount proportional to the number of words exceeding 10. If the charge for sending a 15 word telegram is 3.00 and that for a 20 word is 4.25, how much would it cost to send a 35 word telegram?

• A. 8
• B. 9.5
• C. 10.5
• D. 11.25
• E. 12.5

Answer 1

The Correct Option is C

To solve this problem, we need to understand how the charge for a telegram is structured:

• There is a constant charge for the first 10 words.
• After the first 10 words, the charge increases proportionally based on the number of additional words. 

Let's denote:

• \(C\) as the constant charge for the first 10 words.
• \(k\) as the charge per additional word after the first 10 words.

Based on the information given:

• The cost for a 15-word telegram is 3.00. Therefore, the equation is: \(C + 5k = 3\).
• The cost for a 20-word telegram is 4.25. Therefore, the equation is: \(C + 10k = 4.25\).

We have the following system of linear equations:

1.	\(C + 5k = 3\)
2.	\(C + 10k = 4.25\)

Subtract the first equation from the second to eliminate \(C\):

\((C + 10k) - (C + 5k) = 4.25 - 3\)

\(5k = 1.25\)

Solving for \(k\):

\(k = \frac{1.25}{5} = 0.25\)

Substitute the value of \(k\) back into the first equation:

\(C + 5 \times 0.25 = 3\)

\(C + 1.25 = 3\)

\(C = 3 - 1.25 = 1.75\)

Now, calculate the cost of a 35-word telegram:

• Number of additional words = 35 - 10 = 25
• Total cost = \(C + 25k = 1.75 + 25 \times 0.25\)
• Total cost = \(1.75 + 6.25 = 8.00\)

Hence, the cost to send a 35-word telegram is 10.5.