2 firms make the following charges for renting a car over the weekend .
Firm A - Has a fixed charge of $320, and Charged 50 cents per km for every km over 300
Firm B - has a fixed charge of $60 and charge 70 cents per km traveled .
Find the number of kilometres traveled for which the cost of hiring a car from either firm A or firm B will be the same .
In this case I assumed that the distance traveled will be more than 300 km . And I let it be $x.$
$$320 + (0.5)(x - 300) ) = 60 + (0.7)(x)$$ $$0.5x - 0.7 x = 60 - 170$$
$x = 550$ km
how do I approach this question without having to assume?
Your assumption turns out to be correct, but it is better to prove it. You already know that the price for firm A will be $\$320$ if $x\le300$ km; can you prove that the price for firm B must be less than $\$320$ in such a case?
To see how you erred in finding your answer, expand the expression $$0.5(x-300).$$