A collection of 30 coins consists of dimes and Nickles the total is 1.80 how many dimes are there

So

d=number of dimes

n=number of nickles

so

n+d=30

value=1n=0.05 and 1d=0.1

therefor,

value=0.05n+0.1d

value=1.80

1.8=0.05n+0.1d

mltiply by 100 to make easier

180=5n+10d

divide both sides by 5 to simplify

36=n+2d

so we have

30=n+d and

36=n+2d

30=n+d

multiply by - 1

-30=-n-d

add to other equation

36=n+2d

-30=-n-d +

6=0n+d

6=d

answer is 6 dimes

6 dimes and 24 nickels. Use A+b = 30 and 0.05a + 0.10b = 1.80

and add or subtract those two equations then sub in one variable for the other answer.