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.
Solve word problems leading to linear equations
Let's represent the amount of flour needed for the first cake as x.
According to the problem, the second cake requires 1/2 cup more flour than the first cake. So, the second cake needs x + 1/2 cup of flour.
The third cake requires four times the amount of flour as the first cake, which means it needs 4x cups of flour.
The total amount of flour needed for all three cakes is: x + (x + 1/2) + 4x = 30 1/2
Combining like terms, we have: 6x + 1/2 = 30 1/2
To eliminate the fraction, we can multiply both sides of the equation by 2: 2(6x + 1/2) = 2(30 1/2)
This becomes: 12x + 1 = 61
Subtracting 1 from both sides: 12x = 60
Dividing both sides by 12: x = 5
So, 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.