Answer:
The number of pennies are 6 and number of nickels are 8.
Step-by-step explanation:
Given:
Serenity has $0.46 worth of pennies and nickels.
She has a total of 14 pennies and nickels altogether.
Now, to find the number of pennies and the number of nickels she has.
Let the number of pennies be [tex]x[/tex].
And the number of nickels be [tex]y[/tex].
So, the number of pennies and nickels altogether are:
[tex]x+y=14.[/tex]
[tex]x=14-y.[/tex]........( 1 )
As given total worth = $0.46.
And the value of a penny is $0.01 and the value of a nickel is $0.05.
Now, the total worth of pennies and nickels:
[tex]0.01x+0.05y=0.46[/tex]
Putting the value of equation ( 1 ) in the place of [tex]x[/tex].
[tex]0.01(14-y)+0.05y=0.46[/tex]
[tex]0.14-001y+0.05y=0.46[/tex]
[tex]0.14+0.04y=0.46[/tex]
Subtracting both sides by 0.14 we get:
[tex]0.04y=0.32[/tex]
Dividing both sides by 0.04 we get:
[tex]y = 8.[/tex]
So, the number of nickels = 8.
Now, putting the value of [tex]y[/tex] in equation ( 1 ) we get:
[tex]x=14-8[/tex]
[tex]x=6.[/tex]
Thus, the number of pennies = 6.
Therefore, the number of pennies are 6 and number of nickels are 8.
