Question 113438
F = number of 5c stamps
T = number of 13c stamps
E = number of 18c stamps
{{{T = 2F - 1}}}
{{{E = T + 5}}}
{{{5F + 13T + 18E = 260}}}
{{{5F + 13(2F - 1) + 18E = 260}}}
{{{5F + 13(2F - 1) + 18(T + 5) = 260}}}
{{{5F + 13(2F - 1) + 18(2F - 1 + 5) = 260}}}
{{{5F + 26F - 13 + 36F + 72 = 260}}}
{{{67F + 59 = 260}}}
{{{67F = 260 - 59}}}
{{{67F = 201}}}
{{{F = 3}}}
{{{T = 2F - 1}}}
{{{T = 6 - 1}}}
{{{T = 5}}}
There are 5 thirteen cent stamps in the collection
check:
{{{E = T + 5}}}
{{{E = 10}}}
{{{5F + 13T + 18E = 260}}}
{{{5*3 + 13*5 + 18*10 = 260}}}
{{{15 + 65 + 180 = 260}}}
{{{260 = 260}}}
OK