229k views
3 votes
Isabelle has $5.45 in her purse. If she has five more nickels than dimes, and twice as many quarters than dimes, how many of each type of coin does she have?

User QuokMoon
by
3.6k points

1 Answer

14 votes

Answer:

Nickel = 13

Dimes = 8

Quarters = 16

Explanation:

Let N denote Nickel,

Let D denote dime

Let Q denote quarter

Now, from online conversions;

1 nickel = 5 cents

Also, 1 dime = 10 cents

Also, 1 quarter = 25 cents

Isabelle has $5.45 which is also 545 cents.

Thus, we have;

5N + 10D + 25Q = 545 - - - (eq 1)

We are told that;

she has five more nickels than dimes, and twice as many quarters than dimes.

Thus;

N = D + 5

Also, Q = 2D

Plugging them for N and Q in eq 1 givens;

5(D +5) + 10D + 25(2D) = 545

5D + 25 + 10D + 50D = 545

25 + 65D = 545

65D = 545 - 25

65D = 520

D = 520/65

D = 8

Thus; N = D + 5 = 8 + 5 = 13

Q = 2D = 2 × 8 = 16

User MoMoney
by
3.4k points