Edmond is training for a triathlon and needs to swim a certain distance for today's workout. If he swims at the rec center pool, he will complete a 300-meter warmup and then swim laps in a lane that is 15 meters long. If Edmond swims at the indoor pool at his gym, he will complete a 100-meter warmup, plus a main set that consists of 25 meters per lap. If Edmond swims the correct number of laps, he can complete the same distance in either pool. How many laps will that take?

20 laps

Step-by-step explanation:

Since you are looking for the number of laps that will make him have an equal distance in both pools, you start by making two equations and setting them equal to each other.

So: 300+15x = 100+25x

Then, you simplify it:

300+15x=100+25x

300-100=25x-15x

200=10x

x=20

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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