Question

⑤ how is the value of x related to the value of y? write an equation to describe this.
⑤ determine how many bags of chips and jars of salsa craig bought.
④ there was a total of 34 people at the family reunion. to feed the crowd, 140 oz of pulled pork were prepared. five oz of pulled pork is portioned for each adult and three oz of pulled pork is portioned for each child. let a be the number of adults and c be the number of children at the family reunion.
ⓐ write an equation describing the relationship between a and c.
ⓑ write an equation for the total amount of pulled pork needed in terms of a and c.
ⓒ determine the number of adults and the number of children at the reunion. clearly show your reasoning.

Explanation:

Step1: Analyze the total number of people

The total number of people at the reunion is the sum of adults (\(a\)) and children (\(c\)), and it's given as 34. So the equation for the number of people is \(a + c = 34\).

Step2: Analyze the total amount of pulled pork

Each adult gets 5 oz, so total for adults is \(5a\) oz. Each child gets 3 oz, so total for children is \(3c\) oz. The total pulled pork is 140 oz, so the equation is \(5a + 3c = 140\).

Step3: Solve the system of equations

From the first equation \(c = 34 - a\). Substitute this into the second equation:

$$
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$$

Then substitute \(a = 19\) into \(c = 34 - a\), we get \(c = 34 - 19 = 15\).

Part (a)

Step1: Define the relationship for total people

The total number of people is the sum of adults and children. So \(a + c = 34\).

Part (b)

Step1: Calculate pork for adults and children

Adults: \(5a\) oz, Children: \(3c\) oz. Total is 140 oz, so \(5a + 3c = 140\).

Part (c)

Step1: Substitute \(c = 34 - a\) into pork equation

As done before, solve to find \(a = 19\) and \(c = 15\).

Answer:

Part (a)

The equation for the number of people: \(\boldsymbol{a + c = 34}\)

Part (b)

The equation for pulled pork: \(\boldsymbol{5a + 3c = 140}\)

Part (c)

Number of adults (\(a\)): 19, Number of children (\(c\)): 15