The number of dimes, pennies and nickels are required.
The number of dimes is 50, pennies is 200 and nickels is 75.
Let the number of dimes be [tex]x[/tex]
From the question the number of dimes is one-fourth the number of pennies and two-thirds the number of nickels.
So,
The number of pennies is [tex]4x[/tex]
and number of nickels is [tex]\dfrac{3}{2}x[/tex]
1 nickel = 0.05$
1 penny = 0.01$
1 dime = 0.01$
Total value of the coins is $10.75
[tex]0.1x+0.05\times \dfrac{3}{2}x+0.01\times 4x=10.75\\\Rightarrow 0.215x=10.75\\\Rightarrow x=\dfrac{10.75}{0.215}\\\Rightarrow x=50[/tex]
The number of dimes is 50.
The number of pennies is [tex]4x=4\times50=200[/tex]
The number of nickels is [tex]\dfrac{3}{2}x=\dfrac{3}{2}\times50=75[/tex].
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