To make 4.5 cups of fruity granola, the recipe calls for 1.5 cups of raisins, 1 cup of granola, and 2 cups of blueberries. if you want to make 18 cups of fruity granola, how much of each of the ingredients do you need?

you need 6 cups of raisins, 4 cups of granola and 8 cups of blueberries.

Step-by-step explanation:

Step 1: Find how much raisins are needed

For 4.5 cups of fruity granola, we need 1.5 cups of raisins

For 18 cups of fruity granola, we need y cups of raisins

4.5 : 1.5

18 : y

Cross multiply

4.5y = 1.5 x 18

y = 27/4.5

y = 6 cups of raisins

Step 2: Find how much granola is needed

For 4.5 cups of fruity granola, we need 1 cup of granola

For 18 cups of fruity granola, we need y cups of granola

4.5 : 1

18 : y

Cross multiply

4.5y = 18

y = 4 cups of granola

Step 3: Find how much blueberries are needed

For 4.5 cups of fruity granola, we need 2 cups of raisins

For 18 cups of fruity granola, we need y cups of blueberries

4.5 : 2

18 : y

Cross multiply

4.5y = 2 x 18

y = 36/4.5

y = 8 cups of blueberries

Therefore, in order to make 18 cups of fruity granola, you need 6 cups of raisins, 4 cups of granola and 8 cups of blueberries.

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.

overpriced

step-by-step explanation: