In a salad recipe, the ratio of carrots to cucumbers must remain constant. the table below shows some possible combinations of carrots and cucumbers.
if only whole vegetables can be used, what is the fewest number of vegetables that can be used to make this salad?
a.) 1
b.) 3
c.) 4
d.) 12

Hello there!

The pairs in the table are: 3 carrots to 9 cucumbers, (dividing both sides by 3, we get 1 carrot to 3 cucumbers) wich has a ratio of 1:3.

after we got 4 carrots to 12 cucumbers, we could divide both sides by 4, and we also get a ratio of 1:3

And we can see this for all the pairs in the table, you always need to use cucumbers equal to three times the amount of carrots tat you used.

So if you use one carrot you need to use 3 cucumbers; wich ads to a total of 4 vegetables.

This is the less amount of vegetables that you can use because you can't use less than one carrot. (because you need to use whole vegetables)

Then the correct option is C.

{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

i think the answer is true

step-by-step explanation: