The usual toll charge to use the Bingham tunnel is 50 cents. If you purchase a special sticker for $5.50, the toll is only 35 cents. At least how many trips through the tunnel are needed before the sticker costs less than paying for each trip separately?

Question

The usual toll charge to use the Bingham tunnel is 50 cents.  If you purchase a special sticker for $5.50, the toll is only 35 cents.  At least how many trips through the tunnel are needed before the sticker costs less than paying for each trip separately?

anonymous · Answer

trips taken at usual toll = 0.50 * x = 0.50x
trips taken with sticker = 5.50 + 0.35x

You want to know when they're equal to each other.
0.50x = 5.50 + 0.35x
0.15x = 5.50
x = 5.50/0.15
x = 36 2/3

Check:
0.50x = 0.50 * 36 2/3 = 18 1/3
5.50 + 0.35x = 5.50 + (0.35 * 36 2/3) = 5.50 + 12.8333333 =18 1/3
True