Help with this math question

Question

A party rental company has chair and tables. The total cost to rent 2 chairs and 12 tables is $129.

Answer 1

2c + 12t = 129

one equation 2 unknowns usually means infinite solutions

but c and t have to be integers narrowing down the possibilities

a 2nd major restriction on the solutions

c = $1, t = 127/12= about $10,58

c = $2 t = 125/12 = about$10.42

c= $3 t = 121/12 = about $10.08

c = $4 t = 119/12 = about $9,92

tables cost at least twice chairs, so reasonable odds are

chairs went for from $2 to $4, with tables in the range of $10 to $10 1/2 dollars

c = $5 t = 117/2

c = $6 t = 115/12

c = $7 t = 113/12 = $9,25

c = $8 t= 111/12

c = $10 t = 107/12 = $8,92