Hi.
The key here is that you have to know the value of a quarter and of a nickel. You also have to understand that, whatever the number of nickels that Manuel has, he'll have 14 minus that number of quarters because the total number of coins is 14.
So, since the value of a nickel is 0.05 and the value of a quarter is 0.25 and since we are going to convert 190 cents to $1.90 so that we can keep the decimal places consistent:
0.05x + 0.25(14 - x) = 1.90
0.05x + 3.50 - 0.25x = 1.90
-0.20x = -1.60
x = 8
Manual has eight nickels in his pocket. He must, therefore, have 14 - 8 = 6 quarters in his pocket, too.
Let's see if we are right:
0.05x + 0.25(14 - x) = 1.90
0.05(8) + 0.25(14 - 8) = 1.900
0.40 + 0.25(6) = 1.90
$0.40 + $1.50 = $1.90
That is true, so our answers must be correct!
