Problema Solution

Katonya counted 123 coins in all. She had 23 pennies, the same number of dimes as nickels and 10 more quarters than dimes. How many of each did she have?

Answer provided by our tutors

1 penny = 1 cent

1 nickle = 5 cents

1 dime = 10 cents

1 quarter = 25 cents


let


p = the number of pennies

n = the number of nickels

d = the number of dimes

q = the number of quarters


Katonya counted 123 coins in all


p + n + d + q = 123


She had 23 pennies,


p = 23 pennies


plug p = 23 pennies into p + n + d + q = 123 we get


23 + n + d + q = 123


the same number of dimes as nickels


d = n


10 more quarters than dimes


q = d + 10


by solving the system of equations


23+ n + d + q = 123

d = n

q = d + 10


we find


d = 30 dimes


n = 30 nickles


q = 40 quarters


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