Question 229556: If you have 51¢ and you have the same number of nickels as dimes, what is the minimum number of pennies you can have?
Found 2 solutions by checkley77, drj:
Answer by checkley77(12844)   (Show Source):
Answer by drj(1380)  (Show Source):
You can put this solution on YOUR website! If you have 51¢ and you have the same number of nickels as dimes, what is the minimum number of pennies you can have?
Step 1. Let x be the number of nickels.
Step 2. Let x be the number of dimes since it's the same as the number of nickels.
Step 3. Let 0.05x be the dollar value of nickels
Step 4. Let .10x be the dollar value of dimes.
Step 5. Let 0.05x+0.10x=0.15x be the dollar value of nickels and dimes.
Step 6. Let y be the number of pennies.
Step 7. Let 0.01y be the dollar value of pennies
Step 8. Let 0.15x+0.01y=0.51 since the total value is 51 cents.
Step 9. I started with y=1 (since that is the minimum) and then see if x is an integer. If not, increase y until x is an integer. Finally, it turns out that, y=6, where x is an integer as shown below.
Subtract 0.06 from both sides of the equation
Divide by 
Check dollar value 0.15*3+0.06=0.51 which is a true statement.
Note when x=4, then 0.15*4=0.60 cents...no pennies involve.
Note when x=2, then 0.15*2=0.30 cents but then you have 21 pennies...not a minimum.
Now, that I know the answer, you could have started with x=1 and increase it until you have the smallest amount of pennies.
Step 10. ANSWER: The minimum number of pennies is 6.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Good luck in your studies!
Respectfully,
Dr J
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