A parking meter contains dimes and quarters worth 8.00. There are 41 coins in all. Find how many of each here are.
Solution:-
Let x = the number of dimes and y = the number of quarters.
Translate the second statement into an equation.
x + y = 41
translate the first statement into an equation.
0.10x + 0.25y = 8
Clear the equation of decimals.
10x + 25y = 800
Now you have a system of equations. You may solve the system using either elimination or substitution.
Use substitution and solve the first equation for x.
x + y = 41
x = 41 – y
Substitute 41 – y for x into the second equation and solve.
10x + 25y = 800
10(41 – y) + 25y = 800
410 – 10y + 25y = 800
410 + 15y = 800
15y = 390
y = 26
Substitute 26 for y in the equation x + y = 41 and solve.
x + 26 = 41
x = 15
Therefore are 15 dimes and 26 quarters in the parking meter.