Acollection of dimes and nickels is worth $5.60. the ratio of dimes to nickels is 3: 2. how many dimes and how many nickels are there?

There are 42 dimes and 14 nickels there if the collection of dimes and nickels is worth $5.60

First, we need to convert dimes and nickel to pennies to have:

1 dime = 10 pennies

1 nickel = 5 pennies

Since the ratio of dimes to nickels is 3:2, this shows that we have 30  dimes and 10 pennies

Total pennies  = 30 + 10 = 40 pennies

Since the total collection of dimes and nickels is worth $5.60, this means that the total collections in pennies are 560 pennies ($1 is 100 pennies)

Number of pennies for the ratio of 30 = 30/40 * 560

Number of pennies for the ratio of 30 = 420

Number of dimes = 420/10 = 42 dimes

Number of pennies for the ratio of 10 = 10/40 * 560

Number of pennies for the ratio of 10 = 140

Number of nickel = 140/10 = 14 nickels

Hence there are 42 dimes and 14 nickels there if the collection of dimes and nickels is worth $5.60

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