Note: Consider we need to find each type of coins he has.
Given:
Erin has quarters and nickels for a total of 16 coins.
The value of his coins is $2.60.
To find:
The number of each type of coins.
Solution:
Let x represent the number of quarters and y represent the number of nickels.
According to the question,
Total coins : [tex]x+y=16[/tex] ...(i)
Total value : [tex]0.25x+0.05y=2.60[/tex] ...(ii)
Multiply equation (i) by 0.25 and subtract the result from (ii).
[tex]0.25x+0.05y-0.25(x+y)=2.60-0.25(16)[/tex]
[tex]0.25x+0.05y-0.25x-0.25y=2.60-4[/tex]
[tex]-0.20y=-1.40[/tex]
Divide both sides by -0.20.
[tex]y=7[/tex]
Put y=7 in (i).
[tex]x+7=16[/tex]
[tex]x=16-7[/tex]
[tex]x=9[/tex]
Therefore, the number of quarters is 9 and number of nickels is 7.
