Answer: he has 23 quarters, 31 nickels and 10 dimes.
Step-by-step explanation:
The worth of a quarter is 25 cents. Converting to dollars, it becomes
25/100 = $0.25
The worth of a nickel is 5 cents. Converting to dollars, it becomes
5/100 = $0.05
The worth of a dime is 10 cents. Converting to dollars, it becomes
10/100 = $0.1
Let x represent the number of quarter that he has.
Let y represent the number of nickels that he has.
Let z represent the number of dimes that he has
Steven's quarters total $4.20 more than his nickels. This means that
0.25x = 0.05y + 4.2
Dividing through by 0.05, it becomes
5x = y + 84
y = 5x - 84-- - - - - - - - - -1
His quarters total $4.75 more than his dimes. This means that
0.25x = 0.1z + 4.75
Dividing through by 0.1, it becomes
2.5x = z + 47.5
z = 2.5x - 47.5- - - - - - - - - -2
The total value of the coins is $8.30. This means that
0.25x + 0.05y + 0.1z = 8.3- - - - - - -3
Substituting equation 1 and equation 2 into equation 3, it becomes
0.25x + 0.05(5x - 84) + 0.1(2.5x - 47.5) = 8.3
0.25x + 0.25x - 4.2 + 0.25x - 4.75 = 8.3
0.75x - 8.95 = 8.3
0.75x = 8.3 + 8.95 = 17.25
x = 17.25/0.75
x = 23
Substituting x = 23 into equation 1, it becomes
y = 5 × 23 - 84
y = 31
Substituting x = 23 into equation 2, it becomes
z = 2.5 × 23 - 47.5
z = 10
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