Over the weekend brady and jack drove to key west to go scuba diving. now they're preparing to go home. brady needs gasfor his jeep, which gets 28 mles per gallon for gas mileage. when he stops at the gas station, he already has 10 gallons in his tank. he buys more gas for $1.75 per gallon. if brady spends $17.50 on gas, what is the total distance the boys could travel.

The total distance the boy can travel is 560 miles.

Step-by-step explanation:

Given,

The boy travels with 28 miles per gallon,

That is the distance travel by him for a gallon = 28 miles,

Also, the original quantity of gas he has = 10 gallon,

And, he buys more gas for $1.75 per gallon.

Let x be the quantity of gas bought by him,

⇒ Cost of gas he bought = 1.75x dollars,

According to the question,

1.7x = 17.50 ⇒ x = 10

Thus, he bought 10 gallon gas,

Total quantity of gas he has = 10 + 10 = 20 gallon,

Hence, the distance travelled by him with 20 gallon = 20 × 28 = 560 miles.

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.

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