Question

karl has stamps in his desk drawer. the possible combinations of stamps are shown below.
karls stamp collection

number of 45-cent stamps	number of 65-cent stamps
20	15
22	13
25	10

which statement about the stamps is correct?

• the total number of stamps is 25.
• the total value of the stamps is $18.75.
• the total number of stamps is 35.
• the total value of the stamps is $19.15.

Explanation:

Step1: Analyze total number of stamps

For each row, sum the number of 45 - cent and 65 - cent stamps.

• Row 1: \(18 + 17=35\)
• Row 2: \(20 + 15 = 35\)
• Row 3: \(22+13 = 35\)
• Row 4: \(25 + 10=35\)

So the total number of stamps is always 35 for each combination.

Step2: Analyze total value of stamps (optional, but to check other options)

Take row 1: Value \(=18\times0.45 + 17\times0.65=8.1+11.05 = 19.15\)
Row 2: \(20\times0.45+15\times0.65 = 9 + 9.75=18.75\)
Row 3: \(22\times0.45 + 13\times0.65=9.9+8.45 = 18.35\)
Row 4: \(25\times0.45+10\times0.65 = 11.25+6.5 = 17.75\)
The total number of stamps is constant (35) across all combinations, while the total value varies. The option "The total number of stamps is 25" is wrong, "The total value of the stamps is $18.75" is only true for one combination, "The total value of the stamps is $19.15" is only true for one combination, but "The total number of stamps is 35" is true for all combinations.

Answer:

The total number of stamps is 35.