Question
Ashton is hosting a banquet, he plans to spend 
, plus or minus 
, at a cost of 
per guest. Solve 
to find the maximum and minimum number of guests. If there can be up to 7 guests at each table, what is the minimum number of tables Ashton should reserve so that every guest has a seat?
Hint:
|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by
So, we will get two cases in the solution of the given equation. We simplify the equation as much as possible and then apply the above definition to get the value of x.
For 2nd part, we find the required numbers of tables by dividing the minimum number of guests by 7.
The correct answer is: Hence, we get two values of x satisfying the given equation, x = 14,18
Step by step solution:
The given equation is
Using the definition of absolute value,
We get two possibilities,
Simplifying, we get
Subtracting 400 both sides, we have
Dividing throughout by -3, we get
For 
,
Adding 400 both sides, we get
Dividing by 25 throughout, we get
Hence, we get two values of x satisfying the given equation,
Thus,
Maximum number of guests = 18
Minimum number of guests = 14
Number of guests that can sit on 1 table = 7
Minimum number of guests = 14
Thus, Ashton should reserve 
= 2 tables
Absolute value of a variable has many uses in mathematics. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.
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A company must determine the cost of producing and selling one of its products to create a cost equation. It must also calculate the overhead costs of production. Typically, the cost equation is the cost of manufacturing and selling one item multiplied by the number of items sold and added to the company's overhead costs.
For example, a company with $300,000 in overhead costs that manufacture and sells products that cost the company $5 each has a cost equation of 300,000 + $5. (5 x number of products sold).
"Anna bought 8 tetras and 2 rainbow fish for her aquarium. The rainbow fish cost $6 more than the tetras. She paid a total of $37. Which of the following are true ? Select all that apply ;
A. The cost of 4 tetras is the same as the cost of a rainbow fish.
B. One rainbow fish plus 5 tetras Cost $21.
C. An equation to find the cost r, in dollars of a rainbow fish is 8r + 2(r + 6) = 37
D. Reducing the number of rainbow fish by 1 would result in a total cost of $28.50
E. An equation to find the cost t, in dollars , of a tetra is 8t + 2t + 6 = 37
Let's talk about the cost equation.
A company must determine the cost of producing and selling one of its products to create a cost equation. It must also calculate the overhead costs of production. Typically, the cost equation is the cost of manufacturing and selling one item multiplied by the number of items sold and added to the company's overhead costs.
For example, a company with $300,000 in overhead costs that manufacture and sells products that cost the company $5 each has a cost equation of 300,000 + $5. (5 x number of products sold).
