The Reiter family uses three different-sized scoops to serve mashed potatoes : blobs, globs and gobs (these names are so weird aren't they). 2 blobs are equal to 1 glob, and 5 globs equal 3 gobs of mashed potatoes. A bowl holds 12 gobs of potatoes. How many blobs are there in the bowl? RATIO PROBLEM!!! DUH, DUH, DU.

30 blobs

Step-by-step explanation:

The ratios are:

2 blobs: 1 glob

5 globs: 3 gobs

If the bowl can hold 12 gobs, then we can multiply the 5:3 ratio by 4, to make solving easier. We get the ratio 15:12 and then we need to multiply the 2:1 ratio by 15 to get the answer 30 blobs

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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step-by-step explanation: