Which is more economical when renting a vehicle?

LG's Rent a Car : Php 1500 per day plus Php 35 per kilometer traveled

Rent and Drive : Php 2000 per day plus Php 25 per kilometer traveled

Expert Answers

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It comes down to a question of kilometers traveled.  If we restate Php as $, The comparison is LG: $1,500 + $35n Km vs. Rent and Drive: $2,000 +$25n Km. 

If we compare the two values as an equation we can find the value of n that will make the two rentals the same price:

 `$1500+$35n=$2000+$25n `

We subtract $25n from each side and we get
`$1500+$10n=$2000 `

We subtract 1500 from each side and we get
`$10n=$500 `
Divide each side by $10 and n=50. 

So if you drive exactly 50 km each day, both rentals will cost the same amount.  Then we test the values with bigger and smaller compatible numbers to verify which is cheaper for shorter or longer daily travel distances.  In this case I'll use, 10 km, and 100 km.  If you drive 10 km each day: `$1500+$35xx10=$1850` vs `$2000+$25xx10=$2250 `

So for trips shorter than 50 km each day, LG is the better deal. 

While if you drive 100 km each day `$1500+$35xx100=$5000 ` vs. `$2000+$25xx100=$4500 `

so for trips of longer than 50 km each day Rent and Drive is the better deal. 

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