At the baseball game, the Gregory's bought 5 hot dogs and 2 hamburgers and paid $27.00. The Hart's purchases 3 hot dogs and 4 hamburgers and paid $29.50. How much does 1 hot dog cost?

1 hot dog costs $3.50

Step-by-step explanation:

Represent Hot dog with x and Hamburger with y

Gregory's purchase:

--- (1)

Hart's purchase:

---- (2)

Required

Find x

To do this, we'll make use of the elimination method of solving simultaneous equation.

Start by multiplying (1) by 2

2 * ()

This gives:

---- (3)

Subtract (2) from (3)

- ()

-------------------------

Solve for x

Hence:

1 hot dog costs $3.50

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.

after simplifying it i got: -36.25 as my answer. hope that !