Ralph’s fill dirt and croissant shop in spencer makes both grand and petit croissants. each grand requires 1 ounce of flour and 2 ounces of butter, while each petit requires only 1 4 ounce of flour and 1 3 ounce of butter. it is the end of the month and ralph has only 4 ounces of flour and 6 ounces of butter. ralph calculates how many of each type of croissant he should make in order to use all his ingredients. determine the number of grand croissants ralph calculated?

1

Step-by-step explanation:

let G be the number of grand croisssants, and P the number of petit croissants :

we have that 1 ounce of flour and 2 ounces of butter result in one G.

additionally, we have that 1/4 ounce of flour and 1/3 ounce of butter result in one P.

Ralph has 4 ounces of flour and 6 ounces of butter, If he bakes more than 1 G then he will never use all of his ingredients!, let's see:

1 G:

he now has 3 ounces of flour, and 4 ounces of butter,

now we need to figure out how many P's we would obtain with such amounts:

let x be the number of P's

which is reasonable, Ralph can bake 12 P's,

now with more than 1 G:

2G:

Ralph has now 2 ounces of flour and 2 ounces of butter, now we have to figure out that x is the same using the remaining ingredients

This is impossible.

3G:

he runs out of butter.

There is the answer, he is able to bake 1 grand croissant and 12 petit croissants