Answer:
The number of nickels in the jar is 20.
The number of dimes in the jar is 49.
Step-by-step explanation:
Let us assume the total number of nickels = x
The total number of dimes = y
Total coins = 69 coins
⇒x + y = 69
Now as we know:
1 Nickel = $0.05
and 1 Dime = $0.10
⇒ The value of x nickels = x ( $0.05) = 0.05 x
and The value of y nickels = y ( $0.10) = 0.10 y
Total amount in jar = $5.90 ⇒0.05 x + 0.10 y = $5.90
So, the given system of equation is
x + y = 69 .............. (1)
0.05 x + 0.10 y = 5.90 ....... (2)
Substitute the value of y = 69 - x in (2) , we get:
0.05 x + 0.10 y = 5.90 ⇒ 0.05 x + 0.10 ( 69 - x) = 5.90
or, 0.05 x + 6.9 - 0.10 x = 5.90
or, - 0.05 x = -1.00
⇒ x = 1/0.05 = 20, or x = 20
⇒ y = 69 - x = 69 - 20 = 49
Hence the number of nickels in the jar is 20
and the number of dimes in the jar is 49.
