Each are of quarters and nickels is worth $3.70. There are 22 coins in all How many of there?

First, let's call the number of nickels we have #n# and the number of quarters #q#.

Now we can write two equations which we can use to solve the problem through substitution:

First we know there are 22 coins in total, therefore:

#n + q = 22#

And we know their value is $3.70 so we can write:

#0.05n + 0.25q = 3.70#

Step 1) solve the first equation for #n#

#n + q = 22#

#n + q - color(red)(q) = 22 - color(red)(q)#

#n + 0 = 22 - color(red)(q)#

#n = 22 - q#

Step 2) Substitute #22 - q# for #n# in the second equation and solve for #q#.

#0.05(22 - q) + 0.25q = 3.70#

#(0.05 xx22) - (0.05 xx q) + 0.25q = 3.70#

#1.1 - 0.05q + 0.25q = 3.70#

#1.1 + 0.25q - 0.05q = 3.70#

#1.1 + (0.25 - 0.05)q = 3.70#

#1.1 + 0.20q = 3.70#

#1.1 - color(red)(1.1) + 0.20q = 3.70 - color(red)(1.1)#

#0 + 0.20q = 2.60#

#0.20q = 2.60#

#(0.20q)/color(red)(0.20) = 2.60/color(red)(0.20)#

#(color(red)(cancel(color(black)(0.20)))q)/cancel(color(red)(0.20)) = 13#

#q = 13#

Step 3) Substitute #13# for #q# in the solution to the first equation in Step 1.

#n = 22 - 13#

#n = 9#

Solution:

There are 9 nickels and 13 quarters