Equivalent to 175 cents
She has 5 dimes and 25 nickels
====================================================
Explanation:
n = number of nickels
d = number of dimes
n+d = 30 since she has 30 coins of just these two types
n = 5d because she has five times as many nickels compared to dimes
-----------------
We'll use substitution to solve this system
n+d = 30
5d+d = 30 ... replace n with 5d
6d = 30
d = 30/6 ... divide both sides by 6
d = 5
Sophie has 5 dimes
n = 5d
n = 5*5 ... plug in d = 5
n = 25
Sophie also has 25 nickels
(5 dimes) + (25 nickels) = 30 coins total
This confirms we have the right coin counts.
-------------------
Let's find the value of each stack of coins
1 nickel = 5 cents
25 nickels = 125 cents (multiply both sides by 25)
1 dime = 10 cents
5 dimes = 50 cents (multiply both sides by 5)
(5 dimes) + (25 nickels) = (50 cents) + (125 cents) = 175 cents
175 cents = (175/100) dollars = 1.75 dollars
