The table below shows the amount of flour and eggs you need for making different-sized batches of cookies using the same recipe.
cups of flour number of eggs
batch a 333 222
batch b 999 666
batch c 121212 888
write an equation to describe the relationship between fff, the cups of flour, and eee, the number of eggs.
f=cups of flour
e=# of eggs
sry if its wrong
f = 1.5 • e
First, let us find, from the table, how the amount of ingredients increases for different-sized batches.
If we mark cups of flour with f and number of eggs with e, then in the first batch we had 3f and 2e.
In the second batch we had 9f and 6e. That means that the amount of both ingredients increased three times (3f -> 9f and 2e -> 6e).
In the third batch we had 12f and 8e which means that the amount increased four times from the batch A (3f -> 12f and 2e -> 8e).
Since the amount of both ingredients increased by the same number of times, we can say that the ratio between f and e is constant which makes them proprtional.
This ratio can be written as:
f : e = 3 : 2, or
f : e = 9 : 6, or
f : e = 12 : 8
Either way, the ratio is always the same number:
f : e = 1.5
That means that f = 1.5e or, in other words, number of cups of flour will always be 1.5 times greater than the number of eggs.