Question

homework review sheet. u2 lessons 3 - 5 constant of proportionality and equations

1. a recipe says that 4 chicken thighs serves 2 people. fill in the table with the missing values.
2. this table represents a proportional relationship.

what is the constant of proportionality?
write an equation.
based on the equation, if there are 18 children, how many chicken nuggets do you need?

Explanation:

Step1: Find the ratio for chicken - thighs problem

The ratio of chicken thighs to people is $\frac{4}{2}=2$ (i.e., 2 chicken thighs per person).

Step2: Fill in the missing values for chicken - thighs table

For 10 people, the number of chicken thighs is $2\times10 = 20$. For 12 people, the number of chicken thighs is $2\times12=24$. For 15 chicken thighs, the number of people is $\frac{15}{2}=7.5$. For $x$ chicken thighs, the number of people is $\frac{x}{2}$.

Step3: Find the constant of proportionality for chicken - nuggets problem

The constant of proportionality $k$ in a proportional relationship $y = kx$ (where $y$ is the number of chicken nuggets and $x$ is the number of people) is found by $\frac{y}{x}$. For example, when $x = 3$ and $y = 9$, $k=\frac{9}{3}=3$.

Step4: Write the equation for chicken - nuggets problem

The equation is $y = 3x$, where $y$ is the number of chicken nuggets and $x$ is the number of people.

Step5: Find the number of chicken nuggets for 18 children

Substitute $x = 18$ into the equation $y = 3x$. So $y=3\times18 = 54$.

Answer:

• Chicken - thighs table: 20, 24, 7.5, $\frac{x}{2}$
• Constant of proportionality for chicken - nuggets: 3
• Equation for chicken - nuggets: $y = 3x$
• Number of chicken nuggets for 18 children: 54