In your potions masters cupboard you find 6 litres of frog s

In your potions master\'s cupboard you find 6 litres of frog slime, 13 unicorn airs and 7 cups of nutritional yeast. You wish to brew some potions, using up all of these ingredients. In your magic potions manual you find: (a) Model the problem by a system of linear equations (b) Solve the system to determine what quantity to make of each recipe.

Solution

Let x cauldron be made, y bottles be made, z batches be made.

Therefore, putting balances on

Slime, x+y+z=6

Unicorn hair, 2x+10y+z=13

nutritional yeast, x+3y+z=7.

Thus we have 3 equations and 3 variables.

b) To solve we can substitute x+z=6-y from equation 1 to equation 3,

thus, 6-y+3y=7

2y=1 , y=1/2.

Thus x+z= 6-1/2=11/2.

Using value of y and x+z in equation 2,

2x+10(1/2)+z = 13

2x+5+z=13

x+x+z=8

x+11/2=8

x=5/2.

Thus z=11/2-5/2=3.