Answer :
Number each coins are nickels n = 4, dimes d = 4 and quarter q = 8
Finding unknown quantity using a Mathematical Equation:
In Mathematics, a Linear equation is a statement, that can be used to find an unknown quantity in a given problem. Here to represent the unknown quantity we will use variables like x, y, and so on.
In the given problem,
Peggy has 16 coins in her pocket which are quarters, dimes, and nickels
Let the number of quarters = q
Number of dimes = d
Number of nickels = n
Then the total number of coins = q + d + n = 16 ----(1)
And also given that the number of quarters that she has is equal to the number of dimes plus the number of nickels.
=> q = d + n ----(2)
From (1) and (2)
=> q + q = 16
=> 2q = 16
=> q = 8
substitute q = 8 in (2)
8 = d + n
=> n = 8 - d ----(3)
Given that the total amount that she had = $ 2.60 = 260 cents
As we know nickel = 5 cents, dime = 10 cents, and quarter = 25 cents
=> 25q + 10d + 5n = 260
=> 5q + 2d + n = 52
=> 5(8) + 2d + n = 52
=> 2d + 8 - d = 52 - 40
=> d = 4
From (3), n = 8 - 4 = 4
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