Car rental agency A charges ₹50 per day plus ₹10 per kilometer driven. Agency B charges ₹20 per day plus ₹30 per kilometer driven. For a one-day rental it is cheaper to rent from agency A if you drive more than how much than agency B?
Question
Car rental agency A charges ₹50 per day plus ₹10 per kilometer driven. Agency B charges ₹20 per day plus ₹30 per kilometer driven. For a one-day rental it is cheaper to rent from agency A if you drive more than how much than agency B?
Solution 1
To solve this problem, we need to set up an equation where the cost of renting from Agency A is less than the cost of renting from Agency B.
The cost of renting from Agency A is ₹50 per day plus ₹10 per kilometer driven. So, if you drive x kilometers, the cost would be 50 + 10x.
The cost of renting from Agency B is ₹20 per day plus ₹30 per kilometer driven. So, if you drive x kilometers, the cost would be 20 + 30x.
We want to find the point where it becomes cheaper to rent from Agency A, so we set the two equations equal to each other and solve for x:
50 + 10x = 20 + 30x
Subtract 10x from both sides:
50 = 20 + 20x
Subtract 20 from both sides:
30 = 20x
Divide both sides by 20:
x = 1.5
So, if you drive more than 1.5 kilometers, it would be cheaper to rent from Agency A.
Solution 2
To solve this problem, we need to set up an inequality where the cost of renting from Agency A is less than the cost of renting from Agency B.
Let's denote the number of kilometers driven as 'k'.
The cost for Agency A is ₹50 (daily charge) + ₹10k (charge per kilometer). The cost for Agency B is ₹20 (daily charge) + ₹30k (charge per kilometer).
We want to find the number of kilometers (k) where Agency A's cost is less than Agency B's cost. So we set up the inequality:
50 + 10k < 20 + 30k
Now, we solve for 'k':
First, subtract 20 from both sides to get: 30 + 10k < 30k
Then, subtract 10k from both sides to get: 30 < 20k
Finally, divide both sides by 20 to solve for 'k': k > 1.5
So, it is cheaper to rent from Agency A if you drive more than 1.5 kilometers.
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