Sam has five more dimes than quarters and four fewer nickels than quarters. if he has a total of $4.70, how many of each does he have?

Start be making three equations to represent your amount of each coin, d=5+q and n=q-4. Next, make an equation representing your amount and value of each coin to your total amount, t=.25q+.1d+.05n, with t being your total money. Now, plug in your known values, 4.7=.25q+.1(5+q)+.05(q-4)=.25q+.5+.1q+.05q-.2=.4q+.3, now solve for q, .4q=4.4, q=4.8/.4=11. This gives you your value of quarters as 12. Now, plug q=12 into your equations for d and n, d=5+11=16, n=11-4=7, So you have 11 quarters, 16 dimes, and 7 nickels.

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