The gilbert family bought airline tickets online. each ticket cost $186. the web site also charged a flat fee of $16 for the transaction. the gilberts were charged a total of $1132. write an equation and solve it to determine how many tickets the gilberts purchased

Equation is

The Gilberts purchased 6 tickets

Step-by-step explanation:

x is the number of tickets purchased.

As $186 is the price for each ticket, you multiply 186 by x, to obtain the total amount paid for the tickets (no fees).

Also, you add the flat fee for the transaction that is 16 and as this fee is not depending on the amount of tickets purchased, you add 16 as a fixed number.

Then you have that 186*x+16 is equal to the total cost of the transation that is given and it is $1132.

Then you have the equation:

Next, you isolate the x:

The Gilberts purchased 6 tickets

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

answer: what do you mean