Question

10. The table below shows the proportional relationship between the weight of dog food, in ounces, and the number of packs of dog food
Number of Packs
of dog food Number of Ounces
of dog food
4 96
5 120
6 144
What is the constant of proportionality

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \begin{array}{ccll} \stackrel{x}{packs}&\stackrel{y}{\stackrel{food}{oz}}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 4&96\\ 5&120\\ 6&144 \end{array}\impliedby \textit{we know that } \begin{cases} x=4\\ y=96 \end{cases} \\\\\\ 96=k4\implies \cfrac{96}{4}=k\implies 24=k$