Answer:
Number of dimes = 34
Number of nickels = 13
Step-by-step explanation:
Total number of coins = 47
Coins are in the form of nickels and dimes.
Value of a nickel = 5 cents
Value of a dime = 10 cents
Total value of coins = $4.05 or 405 cents
To find:
Number of nickels and dimes?
Solution:
Let number of nickels = [tex]x[/tex]
Money value of nickels = 5[tex]x[/tex]
Let number of dimes = [tex]y[/tex]
Money value of dimes = 10[tex]y[/tex]
Total value of coins = [tex]5x+10y[/tex]
This value is given as equal as 405.
As per question statement, the equations can be written as:
[tex]5x+10y = 405 ..... (1)\\x+ y = 47 ...... (2)[/tex]
Multiplying equation (2) with 5 and subtracting from equation (1):
[tex]10y - 5y = 405 - 235 \\\Rightarrow 5y = 170\\\Rightarrow y = 34[/tex]
Number of dimes = 34
Number of nickels = 47 - 34 = 13
