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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