Question

if you used 4 cups of sugar how much flour does each recipe need ? What is the constant of proportionality for each situation and what does it mean

Answer 1

1. if you use 1/2 cup of sugar, you need 3/4 cup of flour. To find how many cup of flour do you need for 4 cups of sugar, you can use the next proportion:

`\frac{(1)/(2)\text{cup of sugar}}{4\text{ cup of sugar}}=\frac{(3)/(4)\text{ cup of flour}}{x\text{ cup of flour}}`

Solving for x

`\begin{gathered} (1)/(2)\cdot x=(3)/(4)\cdot4 \\ x=3\cdot2 \\ x=6 \end{gathered}`

You need 6 cups of flour for the first recipe.

Replacing x = 4 into the equation, we get:

`\begin{gathered} y=(7)/(4)\cdot x \\ y=(7)/(4)\cdot4 \\ y=7 \end{gathered}`

You need 7 cups of flour for the first recipe.

2. The constant of proportionality of the table is got dividing the values of the variables. Taking for example, 1/2 cup of sugar and 3/4 cup of flour,

`((3)/(4))/((1)/(2))=(3)/(4)\cdot2=3\cdot(2)/(4)=3\cdot(1)/(2)=(3)/(2)`

the constant is 3/2 for the first recipe.

In the second recipe, the constant is 7/4; as can be seen in the equation

The constant relates the number of flour cups needed for 1 cup of sugar