Calculus / Algebra word problem

Question

You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 600 eggs and 1350 cups of cream. How many quarts of each flavor should you make in order to use up all the eggs and cream? How much of each to use up all the resources ?

Answer 1

The tricky part of a word problem is generally translating to formulas that you already know how to solve. The steps are (1) name the quantities of interest
(2) write the equations relating the quantities
(3) solve

Let v = number of Vanilla quarts
Let m = number of Mocha quarts

So we want
Desired eggs = 600 = 2v+m
Desired cream = 1350 = 3v+3m

At this point, you probably know how to solve these. If not,

Multiply eggs by three
1800 = 6v + 3m
Remember the cream
1350 = 3v + 3m
Subtract
450 = 3v
Solve
v = 150
Substitute into eggs
600 = 2*150 + m
600 = 300 + m
Solve for m
m = 300