Question

Tera has $1.20 worth of change in nickels and dimes. If she has 2 times as many nickels as dimes , how many of each type of coin does she have ?

Answer 1

Tera has 6 dimes and 12 nickels

Explanation:

We can determine how many of each type of coin Tera has using a system of equations, where:

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

First equation:

We know that the worth of the nickels and dimes equals the total worth:

(nickel value * quantity) + (dime value * quantity) = total worth

Since Tera has $1.20 worth of change, a nickel is worth $0.05, and a dime is worth $0.10, our first equation is given by:

0.05N + 0.10D = 1.20

Second equation:

Since Tera has 2 times as many nickels as dimes, our second equation is given by:

N = 2D

Method to solve: Substitution:

Solving for D (the number of dimes):

We can solve for D by substituting 2D for N in the first equation:

0.05(2D) + 0.10D = 1.20

0.10D + 0.10D = 1.20

(0.20D = 1.20) / 0.20

D = 6

Thus, Tera has 6 dimes.

Solving for N (the number of nickels):

Now we can solve for N by plugging in 6 for D in the second equation:

N = 2(6)

N = 12

Thus, Tera has 12 nickels.