Arnold is about to go on a 500-mile car trip. His mechanic recommends that he buy a special highway engine oil that will save him 50 cents in gas for every 25 miles of the trip. This new oil, however, will cost $20. Is it worthwhile for Arnold to buy the oil if he has a coupon for $4 dollars off the price?
figure out how many 25 mile segments there are in this trip. multiply that number by 50 cents. compare that number with $20-$4. If it is larger, then using the special oil makes sense.
for a little puzzle to test your understanding, try to figure out how many cents per 25 miles you would have to save for it to be worth buying the special oil.
20 segments * x cents/segment = $16 — that's the break-even point for purchasing the special oil
$16/20 = $0.8 or 80 cents gas savings per 25 miles to make it worthwhile.
for the second one, if we save 50 cents per 25 miles, and we need to save $16, the number of 25 mile segments to be driven is $16/50 cents = $16/$0.5 = 32 segments, or 32*25 = 800 miles