A student buys 5-cent, 10-cent, and 15-cent stamps, with a total value of $6.70. If the number of 5-cent stamps is 2 more than the number of 10-cent stamps, while the
number of 15-cent stamps is 5 more than one half the number of 10-cent stamps, how
many 15-cent stamps did the student obtain?

The value of the 10 cent stamps is, as you said, , the value of the 5 cent stamps is and the value of the 15 cent stamps is 15(0.5n + 5). These three values add up to the total value of the stamps, namely $6.70.

10n + 5(n+2) + 15 (1/2n + 5) = 6.70

10n +5n + 10 + 15/2n + 75 =670

10n + 5n + 15/2n =585

20n + 10n + 15n = 1170

45n = 1170

N=26

The answer would be 484