Carly is making three cakes for the bake sale. The second cake requires 1/2 cup(s) more flour than the first cake. The third cake requires four times the amount of flour as the first cake. The bag of flour she bought has 30 1/2 cups--exactly the amount she needs. How much flour is needed for each cake? Write an equation then solve.
cups of flour in 1st cake,
cups of flour in 2nd cake,
cups of flour in the 3rd cake
Let x be the amount of flour in the first cake.
The second cake requires 1/2 more flour, so it is x + 1/2.
The third cake requires four times the amount of flour as the first cake, so it is 4x.
The total amount of flour needed for the three cakes is: x + (x + 1/2) + 4x = 30 1/2.
Combining like terms, we get 6x + 1/2 = 30 1/2.
Subtracting 1/2 from both sides, we get 6x = 30.
Dividing both sides by 6, we get x = 5.
Thus, the first cake requires 5 cups of flour.
The second cake requires 5 + 1/2 = 5 1/2 cups of flour.
The third cake requires 4(5) = 20 cups of flour. Answer: \boxed{5, \frac{5}{2}, 20}.