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4 votes
Sophie has 30 coins, all nickels and dimes.

She has five times as many nickels as
dimes. How much money does she have?

User EdChum
by
5.7k points

1 Answer

5 votes

Answer: 1.75 dollars

Equivalent to 175 cents

She has 5 dimes and 25 nickels

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Step-by-step 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

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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

User Conic
by
5.3k points
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