Lzzy has three more quarters ($0.25) than she has dimes ($0.10), twice as many nickels ($0.05) as she has dimes, and four times as many pennies ($0.01) as she has dimes.
Let us assume number of dimes = x.
"Three more quarters than dimes" would be = (x+3) quarters .
"Twice as many nickels as dimes " would be = (2x) nickels.
"Four times as many pennies as dimes" would be =(4x) pennies.
Total value of all coins = $7.61.
We can setup an equation now.
0.10*x + 0.25(x+3) + 0.05(2x)+0.01(4x)=7.61.
Let us simplify the equation.
0.10x + 0.25x + 0.75 + 0.10x + 0.04x = 7.61
0.49x + 0.75 = 7.61.
Subtratcing 0.75 from both sides, we get
0.49x = 6.86
Dividing both sides by 0.49, we get
x= 14.
Therefore,
Number of dimes = x = 14.
Number of quarters = (x+3) = 14+3 = 17.
Number of nickels = 2x = 2*14 = 28.
Number of pennies = 4x = 4*14 = 56.
