1) x - number of nickels
2x - 1 - number of dimes
y - number of quarters
Altogether number of coins: x+2x-1+y =25, or 3x - 1 +y =25, 3x+y=26
2) 5x + 10(2x - 1) +25y = 490 (cents)
5x + 20x - 10 +25y = 490
25x +25y=500
x+y=20
3) Now, we need to solve a system of equations.
3x+y=26
x+y=20 → y=20 - x
3x+y=26 → 3x + 20 - x =26 → 2x = 6 → x= 3 (nickels)
y=20 - x → y =20 - 3 = 17 (quarters)
2x - 1 = 2*3 - 1 = 5 (dimes)
So, we have 3 (nickels), 17 (quarters), 5 (dimes).
