Question

. 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?

Answer 1

Answer:

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

$1/4*x = 3=>x=12\\ 1/3*x=4=>x=12$

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

$1/4*x = 2=>x=8\\ 1/3*x=2=>x=6$

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