Answer:
75 number of quarters
150 number of nickels
35 number of dimes
Step-by-step explanation:
Let x, y and z be the amount of quarters, nickel and dimes respectively.
he learns that he has 260 coins, thus;
x + y + z = 260 - - - (1)
Now, we are told that he has twice as many nickels as quarters.
Thus, number of nickels = 2x
y = 2x - - - (2)
From online research, we have the following cost;
1 quarter = $0.25
1 nickel = $0.05
1 dime = $0.1
Total cost is $29.75. Therefore;
0.25x + 0.05y + 0.1z = 29.75 - - - (3)
Put 2x for y in eq (1) and eq (3) to get;
x + 2x + z = 260
3x + z = 260 - - - (eq 4)
0.25x + 0.05(2x) + 0.1z = 29.75
0.25x + 0.10x + 0.1z = 29.75
0.35x + 0.1z = 29.75 - - - (eq 5)
From eq(4), z = 260 - 3x
Thus;
0.35x + 0.1(260 - 3x) = 29.75
0.35x + 26 - 0.3x = 29.75
0.05x = 29.75 - 26
0.05x = 3.75
x = 3.75/0.05
x = 75
So, z = 260 - 3(75)
z = 260 - 225
z = 35
Since y = 2x,
Then,y = 2(75) = 150
Thus,we have;
75 number of quarters
150 number of nickels
35 number of dimes
