Given:
In 16 coins some coins are dimes and some are nickels.
The combined value of her nickels and dimes is 1.35.
To find:
The number of nickels and dimes.
Solution:
We have,
Number of total coins = 16
Combined value = $1.35
Let x be the number of nickels and y be the number of dimes.
Total coins: [tex]x+y=16[/tex] ...(i)
We know that,
1 nickel = $0.05
1 dime = $0.10
Combined value: [tex]0.05x+0.10y=1.35[/tex] ...(ii)
From (i), we get
[tex]y=16-x[/tex] ...(iii)
Putting this in (ii), we get
[tex]0.05x+0.10(16-x)=1.35[/tex]
[tex]0.05x+1.60-0.10x=1.35[/tex]
[tex]-0.05x=1.35-1.60[/tex]
[tex]-0.05x=-0.25[/tex]
Divide both sides by -0.05.
[tex]x=\dfrac{-0.25}{-0.05}[/tex]
[tex]x=5[/tex]
Putting x=5 in (ii), we get
[tex]y=16-5[/tex]
[tex]y=11[/tex]
Therefore, the number of nickels is 5 and the number of dimes is 11.
