Problema Solution
Carly is making three cakes for the bake sale, the second cake requires 1/2 cup more flour than the first one. The third cake requires the same amount of flour as the first cake. The two pound bag of flour she bought has 8-1/2 cups, exactly the amount she needs. How much flour is needed for each cake?
Answer provided by our tutors
let
x = cups of flour for the first cake
y = cups of flour for the second cake
z = cups of flour for the third cake
the second cake requires 1/2 cup more flour than the first one
y = 1/2 + x
the third cake requires the same amount of flour as the first cake
z = x
the two pound bag of flour she bought has 8 1/2 cups = 17/2 cups is exactly the amount she needs
x + y + z = 17/2
by solving the system of equations
y = 1/2 + x
z = x
x + y + z = 17/2
we find
x = 8/3 = 2 2/3 cups
y = 19/6 = 3 1/6 cups
z = 8/3 = 2 2/3 cups
click here to see the step by step solution of the system of equations
2 2/3 cups of flour are needed for the first cake.
3 1/6 cups of flour are needed for the second cake.
2 2/3 cups of flour are needed for the third cake.