Question

a catering company is setting up for a high school graduation party. they expect 150 people to attend. they can provide small tables that seat 6 people and large tables that seat 10 people.
a. find a combination of small and large tables that seats exactly 150 people.
b. let x represent the number of small tables and y represent the number of large tables. write an equation to represent the relationship between x and y.
c. explain what the point (20,5) means in this situation.
d. is the point (20,5) a solution to the equation you wrote? explain your reasoning.
which equation has the same solution as 10x - x + 5 = 41?
a. 10x + 5 = 41
b. 10x - 5 + x = 41
c. 9x = 46
d. 9x + 5 = 41

Explanation:

Step1: Simplify the left - hand side of the equation \(10x - x+5 = 41\)

Combine like terms: \(10x−x=(10 - 1)x=9x\), so the equation becomes \(9x + 5=41\)

Step2: Analyze each option

• Option A: \(10x + 5=41\). The coefficient of \(x\) is wrong. Since \(10x−x = 9x\) in the original equation, this is incorrect.
• Option B: \(10x−5 + x=41\) simplifies to \(11x−5 = 41\), which is not equivalent to the simplified original equation \(9x + 5=41\)
• Option C: \(9x=46\) is not equivalent to \(9x + 5=41\) (subtracting 5 from both sides of \(9x + 5=41\) gives \(9x=36\))
• Option D: \(9x + 5=41\) is exactly the simplified form of the original equation \(10x - x+5 = 41\)

Answer:

D. \(9x + 5 = 41\)