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11111nata11111 [884]
3 years ago
10

There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels there are 3 dimes. For every 2 dimes ther

e are 5 quarters. There are 500 coins in total.
a. How many nickels, dimes, and quarters are in the piggy bank? Explain you reasoning.

b. How much are the coins in the piggy bank worth?
Mathematics
1 answer:
rodikova [14]3 years ago
7 0

Answer: a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.

b) The coins are worth of 91 dollars i.e. $91 in the piggy bank.

Explanation:

Since we have given that

For every 2 nickels there are 3 dimes ,

So, their ratio will be 2:3

and for every 2 dimes there are 5 quarters.\,

So, their ratio will be 2:5

Now, we'll first find the ratio of nickles to dimes to quarters i.e.

Nickle  Dimes  Quarters

2            3

             2               5

So, it becomes ,

Nickle : Dimes : Quarters

2×2     : 3×2        : 3×5

4         : 6            :  15

Now, let the number of nickle be 4x

Let the number of dimes be 6x

Let the number of quarters  be 15x

According to question,

4x+6x+15x=500\\\\25x=500\\\\x=\frac{500}{25}=20

So, number of nickels is given by

4x=4\times 20=80

Number of dimes is given by

6x=4\times 20=120

Number of quarters is given by

15x=4\times 20=300

As we know that

1\ nickel=5\ cents\\\\1\ dime=10\ cents\\\\1\ quarter=25\ cents

So, According to our question, we get

80\times 5+120\times 10+300\times 25=400+1200+7500=9100\ cents\\\\1\ cent=0.01\ dollar\\\\9100\ cents=9100\times 0.01\ dollars=91\ dollars.

Hence,

a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.

b) the coins are worth of 91 dollars i.e. $91 in the piggy bank.


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