Oliver has an equal positive number of quarters, dimes, and pickles in his bag. the total amount in the bag is a whole number of dollars. what is the smallest amount of money stan could have?

side note:
explain as i want to fully understand the answer.

answer:

$3

step-by-step explanation:

dimes = 10c

quarters = 25c

nickels = 5c

find the lcm least common multiple by listing them until they have a common one.

dimes -->       10, 20, 30, 40, 50

quarters -->   25, 50, 75, 100

nickels -->     5, 10, 15, 20, 25, 30, 35, 40, 45, 50

50 is the lowest common multiple. there needs to be a 50c worth of each type of coin.

the term number in the lcm list is the amount of each coin we have:

5 dimes, 2 quarters, 10 nickels.

multiply the amount of each coin by the coin type and add them together to find the total value:

5*10 + 2*25 + 10*5

= 50 + 50 + 50

= 150

150c = $1.50

that is not a whole number.

multiply the value 2 and it will be a whole number.

instead, we now have 10 dimes, 4 quarters and 20 nickels. $1 of each coin type.

either stan or oliver has 300c, or $3.

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.

fahrenheit

step-by-step explanation:

fahrenheit is more precise than celsius. the ambient temperature on most of the inhabited world ranges from -20 degrees fahrenheit to 110 degrees fahrenheit—a 130-degree range. on the celsius scale, that range is from -28.8 degrees to 43.3 degrees—a 72.1-degree range. this means that you can get a more exact measurement of the air temperature using fahrenheit because it uses almost twice the scale.