Given, Bodhi has a collection of 175 dimes and nickel. If she has n numbers of nickel. Then,
The number of dimes coin= 175-n.
The collection is worth $13.30.
1 nickel is worth five cents. So, n nickel will worth 0.05n.
Similarly 1 dime is worth 10 cents. So, 175-n dimes will worth 0.1(175-n).
Since the total worth is $13.30. So, we can set the equation as follows:
0.1(175-n)+0.05n=13.30.
17.5-0.1n+0.05n= 13.30 (By distributing property)
17.5-0.05n=13.30 (Combine the like terms)
-0.05n=13.30-17.5 (Subtract 17.5 from each sides).
-0.05n=-4.2
-0.05n/-0.05=-4.2/-0.05 ( Divide each sides by -0.05)
n=84
So, there is 84 coins in the collection.