Andy has 26 coins made up of quarters and half dollars, and their total value is $11.50. How many quarters does he have?

44 quarters is what he has the 50 cent is a half dollar

X = number of quarters

y = number of half

x + y = 26 = > y = 26 - x

x * $0.25 + y * $0.5 = $11.50

so

x * 0.25 + (26 - x) * 0.5 = 11.5

x * (0.25 - 0.5) = 11.5 - 26*0.5

x * (-0.25) = 11.5 - 13 = - 1.5

x = (-1.5) / (-0.25) = 6

He have 6 quarters and 20 half dollars