Answer:
Total number of dimes collected = 50
Step-by-step explanation:
Let the number of dimes collected = d
And the number of nickels collected = n
On day collection in nickels and dimes = $6.55
Since, 1 nickel = $0.05
Therefore, 'n' nickels = 0.05n
And 1 dimes = $0.10
Value of 'd' dimes = $0.10d
Total value of 'n' nickels and 'd' dimes = $(0.05n + 0.10d)
So the equation for the total value will be,
0.05n + 0.10d = 6.55
5n + 10d = 655 --------(1)
Number of nickels was 6 more than half the number of dimes.
n = [tex]\frac{d}{2}[/tex] + 6 ------(2)
By substituting the value 'n' from equation (2) to equation (1)
5([tex]\frac{d}{2}[/tex] + 6) + 10d = 655
[tex]\frac{5d}{2}[/tex] + 30 + 10d = 655
[tex]\frac{25d}{2}[/tex] = 655 - 30
25d = 625 × 2
d = [tex]\frac{1250}{25}[/tex]
d = 50
Therefore, total number of dimes collected = 50
