Carly is making three cakes for the bake sale. The second cake requires
1 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
31 1/2 cups--exactly the amount she needs. How much flour is needed for each cake? Write an equation then solve.
Let's say the amount of flour needed for the first cake is x cups.
The second cake requires 1 1/2 cups more flour than the first cake, so it needs x + 1 1/2 cups.
The third cake requires four times the amount of flour as the first cake, so it needs 4x cups.
The total amount of flour needed is x + (x + 1 1/2) + 4x = 31 1/2 cups.
Combining like terms, we can simplify the equation to 6x + 1 1/2 = 31 1/2.
Subtracting 1 1/2 from both sides, we get 6x = 30.
Dividing both sides by 6, we find that x = 5.
Therefore, the first cake requires 5 cups of flour, the second cake requires 5 + 1 1/2 = 6 1/2 cups of flour, and the third cake requires 4 * 5 = <<4*5=20>>20 cups of flour.
Let's assume that the amount of flour needed for the first cake is x cups.
According to the information given, the second cake requires 1 1/2 cups more flour than the first cake. So, the amount of flour needed for the second cake is x + 1 1/2 cups.
The third cake requires four times the amount of flour as the first cake. Therefore, the amount of flour needed for the third cake is 4x cups.
According to the problem, the sum of the flour needed for all three cakes is equal to the amount of flour Carly bought, which is 31 1/2 cups.
So, we can write the equation as:
x + (x + 1 1/2) + 4x = 31 1/2
Now, let's solve the equation step by step.
Combine the like terms:
6x + 1 1/2 = 31 1/2
Subtract 1 1/2 from both sides:
6x = 30
Divide both sides by 6:
x = 5
Therefore, the amount of flour needed for the first cake is 5 cups.
To find the amount of flour needed for the second cake, substitute the value of x into the equation:
x + 1 1/2 = 5 + 1 1/2 = 6 1/2
Thus, the amount of flour needed for the second cake is 6 1/2 cups.
To find the amount of flour needed for the third cake, substitute the value of x into the equation:
4x = 4 * 5 = 20
Thus, the amount of flour needed for the third cake is 20 cups.