Katie is making hair clips to sell at the craft fair. to make each hair clip, she uses one barrette and one pre-cut ribbon. the barrettes are sold in packs of 12 and the precut ribbons are sold in packs of nine. how many packs of each item does she need to make the least number of hair clips with no supplies left over?

She needs 3 packs of barrettes and 4 packs of ribbons

Step-by-step explanation:

Consider the provided information.

The barrettes are sold in packs of 12 and the precut ribbons are sold in packs of nine.

We need to find the number of packs of each item does she need to make the least number of hair clips with no supplies left over.

In order to solve this find the LCM of 12 and 9.

12=2×2×3

9=3×3

Thus the LCM of 12 and 9 is 2×2×3×3=36

She needs 36 barrettes  and ribbons so that no supplies left over.

The barrettes are sold in packs of 12, thus she need 3 pack of barrettes.

The precut ribbons are sold in packs of nine, thus it required 4 packs of ribbon.

Hence she needs 3 packs of barrettes and 4 packs of ribbons

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{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1