A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey. Invent a new version of this lemonade recipe that would make more lemonade but taste the same as the original recipe. *

The new version contains 15 lemons, 6 cups of water and 6 tablespoons of honey

Step-by-step explanation:

The given ingredients used to make the lemonade are;

The number of lemons = 5

The number of cups of water = 2

The number of tablespoons of honey = 2

Therefore a new version the lemonade recipe that would make more lemonade but that would still taste the same as the lemonade made with the given recipe is found by scaling up the quantities of the ingredients in the given recipe as follows;

The  ingredients used to make the new lemonade are obtained by multiplying the ingredients in the given recipe by a factor larger than 1;

The number of lemons in the new recipe = 5 × 3 = 15

The number of cups of water in the new recipe = 2 × 3 = 6

The number of tablespoons of honey  in the new recipe = 2 × 3 = 6

The new version contains 15 lemons, 6 cups of water and 6 tablespoons of honey.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

an = 22 + (n-1) *6

110 seats

step-by-step explanation:

an=a1+(n-1)(d)

a1 = 22   this is the first item in the sequence

d =6   this is how the sequence goes up

a)   an = 22 + (n-1) *6

b) a12 = 22 + (12-1) *6

    a12 = 22+11*6

  a12 = 22 +88

  a12 = 110