It takes 3/4 a cup of sherbet per 1 1/4 cup of gingerale to make punch. how much sherbet is needed per cup
of gingerale?

6/10 of a cup

Step-by-step explanation:

If you add 3/4 to sherbet and 1 1/2 cup of to gingerale and keep going you will eventually get to 3 cups of sherbet and 5 cups of gingerale. Now, if you divide 3 by 5 you will get 0.6 or 6/10 of a cup. You would divide because you are trying to find how much sherbet PER ONE CUP of gingerale.

{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