Question

gaby's piggy bank contains nickels and dimes worth 4.90$. If she has 71 coins in total, how many of each does she have?

Answer 1

Gaby has 27 dimes in her piggy bank.

Gaby has 44 nickels in her piggy bank.

Explanation:

We can use a system of equations to determine the number of nickels and dimes Gaby has, where:

• N represents the number of nickels,
• and D represents the number of dimes.

First equation:

We know that the sum of the worth of the nickels ($0.05 * quantity) and dimes ($0.10 * quantity) equals the total worth of 4.90:

(0.05 * quantity) + (0.10 * quantity) = 4.90

Thus, our first equation is given by:

0.05N + 0.10D = 4.90

Second equation:

• We also know that the sum of the nickels and dimes equals 71.

Thus, our second equation is given by:

N + D = 71

Method to solve: Substitution:

First, we can isolate N in the second equation:

(N + D = 71) - D

N = -D + 71

Solving for D (the number of dimes):

Now we can substitute -D + 71 for N in the first equation to solve for D (the number of dimes):

0.05(-D + 71) + 0.10D = 4.90

-0.05D + 3.55 + 0.10D = 4.90

(0.05D + 3.55 = 4.90) - 3.55

(0.05D = 1.35) / 0.05

D = 27

Thus, Gaby has 27 dimes in her piggy bank.

Solving for N (the number of nickels):

Now we can solve for N by plugging in 27 for D in the second equation:

(N + 27 = 71) - 27

N = 44

Thus, Gaby has 44 nickels in her piggy bank.

Answer 2

• 44 nickels
• 27 dimes

Explanation:

You want to know the number of nickels and dimes if 71 coins have a value of $4.90.

Setup

Let d represent the number of dimes (the higher-value coin). Then 71-d is the number of nickels, and their value in cents is ...

10d +5(71 -d) = 490

Solution

Simplifying, we have ...

5d +355 = 490

5d = 135 . . . . . . . . subtract 355

d = 27 . . . . . . . . divide by 5

n = 71 -d = 71 -27 = 44

Gaby has 44 nickels and 27 dimes.

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