Let y represent the number of quarters —————————————————————
Value Value Type Number of of of of each all Coin Coin Coin Coin ————————————————————— Nickels | x | $0.05 | $0.05x Quarters | y | $0.25 | $0.25y ————————————————————— Totals 28 ——— $2.20 •••••••••••••••••••••••••••••••••••••••••••••••••
The first equation comes from the “Number of coins” column.
(Number of nickels) + (Number of quarters) = (total number of coins)
Equation: x + y = 28 ————————————————————— The second equation comes from the “value of all coins” column.
(Value of all nickels) + (Value of all quarters) = (Total value of all coins)
0.05x + 0.25y = 2.20
Remove the decimals by multiplying each term by 100:
5x + 25y = 220 ————————————————————— So we have the system of equations:
{x + y = 28 {5x + 25y = 202
Solve by substitution. Solve the first equation for y:
