Answer:
[tex]n+d=30[/tex] and
[tex]0.05n+0.10d=2.20[/tex]
Step-by-step explanation:
Let n represent the number of nickels
Let d represent the number of dimes.
Luis has a total of 30 coins; equation becomes:
[tex]n+d=30[/tex]
or [tex]n=30-d[/tex] ..... (1)
The value of the coins is $2.20 ; equation becomes:
{a dime is worth 10 cents and a nickel is 5 cents}
[tex]0.05n+0.10d=2.20[/tex] ..... (2)
Putting the value of n from (1) in (2)
[tex]0.05(30-d)+0.10d=2.20[/tex]
=> [tex]1.5-0.05d+0.10d=2.20[/tex]
=> [tex]0.05d=2.20-1.5[/tex]
=> [tex]0.05d=0.7[/tex]
=> d=14
And n=30-d
so, [tex]n=30-14=16[/tex]
So, the system of equations used to determine the number of nickels and the number of dimes Luis has are :
[tex]n+d=30[/tex] and
[tex]0.05n+0.10d=2.20[/tex]
