Question

whitney has a coin jar with a small collection of nickels and dimes. there are 69 coins in the jar. they have a value of $5.90. how many nickels and dimes are in the jar? use substitution to solve.​

Answer 1

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.