## nikkijoy 2 years ago 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?

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1. whpalmer4

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.

2. nikkijoy

500/25

3. whpalmer4

500/25 = ?

4. nikkijoy

20

5. whpalmer4

Great. How much is 20 * 50 cents?

6. nikkijoy

1000

7. whpalmer4

how many dollars is that?

8. nikkijoy

10?

9. whpalmer4

you're not sure? how many cents in a dollar?

10. nikkijoy

100

11. whpalmer4

how much is 20 set of 2 quarters?

12. whpalmer4

\$10, right?

13. nikkijoy

right

14. whpalmer4

so, does it make sense to buy the special oil?

15. nikkijoy

no

16. whpalmer4

you can save \$10 over the course of the trip. would you pay \$16 for that?

17. whpalmer4

good :-)

18. nikkijoy

thankyou

19. whpalmer4

you're welcome.

20. whpalmer4

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.

21. whpalmer4

or how far you would have to drive with this oil for it to be worth it...

22. nikkijoy

hmmm 12.50

23. whpalmer4

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

24. nikkijoy

ohhh okay i jus did 25/2 lol silly me