Question

A cereal company claims that the relationship between the number of cups of cereal and the number of raisins is proportionalComplete the table to show the relationship between the numbers of cups or cereal And the number of raisins based on the company’s claim3|3605|600916

Answer 1

First, determine the constant of proportion for each ordered pair.

Let y be the number of raisins

x be the number of cups of cereal

Solve for the constant of proportion k

`\begin{gathered} y=kx \\ \\ \text{Using \lparen3,360\rparen} \\ y=kx \\ 360=k(3) \\ 360=3k \\ (360)/(3)=(3k)/(3) \\ k=120 \\ \\ \text{Using \lparen5,600\rparen} \\ y=kx \\ 600=k(5) \\ 600=5k \\ (600)/(5)=(5k)/(5) \\ k=120 \end{gathered}`

The constant of proportion is k = 120. Use this information to determine the number of raising for x = 9 and x = 16.

`\begin{gathered} \text{If }x=9,\text{ then} \\ y=kx \\ y=(120)(9) \\ y=1080 \\ \; \\ \text{If }x=16,\text{ then} \\ y=kx \\ y=(120)(16) \\ y=1920 \end{gathered}`

Therefore, we have the following ordered pair in the table (9,1080) and (16,1920).