Let X = the number of dimes and let Y = the number of quarters.
Then X + Y = 185 or X = 185 -Y
$26 is equal to 2600 cents . . . because 1 dollar equals 100 cents.
So 10X + 25Y = 2600
You could also say that .1X + .25Y = 26 but it's easier to not work with decimals.
Now substitute 185 - Y for X
10(185 - Y) + 25Y = 2600
Distribute 10 over the contents of the parentheses . . .
1850 - 10Y + 25Y = 2600
Subtract 1850 from both sides and add the Y terms--> 15Y = 750
Divide both sides by 15--> Y = 50
Plug this into the first equation to solve for X--> X = 185 - 50
X = 135
Plug these numbers into the second equation to see if they work.