Luis has 58 coins in nickels, dimes, and quarters. The number of nickels is three less than twice the number of dimes. The total value of the coins is $7.40. How many of each type of coin does Luis have?

Using the letters Q, N and D for the numbers of quarters nickels and dimes we can write:

Q+N+D=58 coins.

25Q+5N+10D=740 cents.

N=2D-3.

So Q+2D-3+D=58, Q=61-3D. And 25(61-3D)+5(2D-3)+10D=740.

Therefore, 1525-75D+10D-15+10D=740.

1510-55D=740, divide through by 5: 302-11D=148, 11D=154, so D=14, N=28-3=25, Q=61-42=19.

A quick check shows there are 58 coins=19+25+14, value is 4.75+1.25+1.40=$7.40.

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