A plumber charges $50 for every house call and an additional $70 for each hour of work. For one house call yesterday, the plumber earned $435. Which equation can be solved to find the number of hours the plumber worked on the house call?
Let $h$ be the number of hours the plumber worked on the house call. The plumber earned $435, which is $50$ dollars for the house call and $70h$ dollars for $h$ hours of work. Hence, $$435 = 50 + 70h.$$Subtracting 50 from both sides, we have $385 = 70h$. Dividing both sides by 70, we find $h=\frac{55}{7}$ hours. Since the plumber only worked a whole number of hours, we know that $h$ is not an integer. Thus, the plumber didn't work on the house call and we see that this problem has no solution.
This can also be seen by noticing that the amount of money the plumber earned is a multiple of 5 (since it ends in a 5), but the number of hours the plumber worked cannot be a multiple of 5 (since 5 does not divide 7). Thus, there are no whole numbers of hours the plumber could have worked.