1) When Lucas dumped the coins out of his piggy bank, he noticed that there were only nickels and dimes, and the number of nickels was twice the number of dimes. If there were 50 nickels, what was the total value of the coins Lucas dumped out of his piggy bank?

2) When Franco dumped the coins out of his piggy bank, he noticed that there were only nickels and quarters, and the number of quarters was six more than half the number of nickels. If the total value of the coins Franco and Lucas dumped out of each piggy bank was the same, how many coins did Franco dump out of his piggy bank?

3) When Callie dumped the coins out of her piggy bank, she noticed that there were only nickels, dimes and quarters. The number of dimes was one more than twice the number of quarters, and there were half as many quarters as nickels. The coins dumped out of Callie’s piggy bank had a total value equal to that of the coins dumped out of Franco’s and Lucas’ piggy banks combined. What was the total value of the nickels and dimes dumped out of Callie’s piggy bank?

**Answers for question1**

There are only 2 types of coin can be found in the Lucas’ piggy bank, nickels and dimes. And, the number of the nickels was twice the number of dimes. Depend on those conditions, we will have

*Define num_of_nickels as Integer *

*Define num_of_dims as Integer *

*num_of_nickels = 2 * num_of_dimes*

If there were 50 nickels, the total value of the coins Lucas dumped out of his piggy bank will be

*num_of_nickels * $0.05 + num_of_dimes*$0.1, that introduce to*

*num_of_nickels * $0.05 + num_of_nickels/2*$0.1, and to*

*50*$0.05 + 50/2*$0.1 = $2.5 + $2.5 = $5*

**Answers for question2**

There are only 2 types of coin can be found in the Franco’ piggy bank, nickels and quarters.

*num_of_quarters=num_of_nickels/2+6*

total value of the coins Franco and Lucas dumped out of each piggy bank was the same

Depend on the answer of question1, the Lucas’ piggy bank has **$****5, **so that introduce to:

the value of the total coins from Franco piggy bank is **$5**

num_of_nickels*$0.05+num_of_quarters*$0.2=**$5**

num_of_nickels*$0.05+(*num_of_nickels/2+6*)*$0.25=**$5**

num_of_nickels*(0.05+0.125)=5-1.5

num_of_nickels=3/0.175

num_of_nickels=**20**

num_of_quarters=20/2+6=**16**

total number of the coin in Franco piggy bank is **20+16=36**

References

Three Little Piggy Banks http://mathcounts.org, Retrieved on 2014-10-24

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