Question
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.
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.
Answers
GPT 3.5
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.
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.