10 ! premier tire sells three categories of tires: good, better, and best. the good tires cost $106, the better tires cost $156, and the best tires cost $190. the good tires sell 3 times as fast as the best tires and the better tires sell 2.5 times as fast as the best tires. if the total amount of tire sales in january was $233,480, how many of each category of tire was sold? (round your answer to the nearest whole number.)

Let g, b, t represent the numbers of good, better, best tires sold. The problem statement gives rise to 3 equations.
.. 106g +156b +190t = 233,480
.. g -3t = 0
.. b -2.5t = 0

You can put these equations into your friendly equation solver to find
.. g = 780
.. b = 650
.. t = 260 (no rounding necessary)

780 good tires were sold
650 better tires were sold
260 best tires were sold

_____
If you want to solve these equations "by hand," substitution will work well. Substitute for b and g and solve for t. Then the values of b and g fall out immediately.
.. 106(3t) +156(2.5t) +190t = 233480