You are temporarily working for a factory that produces two types of beverages (

Question

You are temporarily working for a factory that produces two types of beverages (beverage A and beverage B). When creating the product, you mix two secret ingredients (secret ingredient 1 and secret ingredient 2) to a base mixture (batch) before bottling the beverage. Into each batch of beverage A,3 gallons of secret ingredient 1 and 2 gallons of secret ingredient 2 is added. Into each batch of beverage B,2 gallons of secret ingredient 1 and 4 gallons of secret ingredient 2 is added. If the factory has 1,200 gallons of secret ingredient 1 and 1,000 gallons of secret ingredient 2 in stock, then how many batches of each beverage should be made so as to use up all the stock of the secret ingredients ? show in detail how you arrived at your solution.

Explanation / Answer

You just have to set up two equations. a and b are the variables for each batch. 3a + 2b = 1200 2a + 4b = 1000 Then you just need to solve this for a and b. The easiest way is probably to use elimination. I'll multiply the second equation by -3/2 to eliminate it. (-3/2)(2a + 4b = 1000) => -3a - 6b = -1500 So now you have: 3a + 2b = 1200 -3a - 6b = -1500 When added together, this gives 0a - 4b = -300. Divide both side by -4 and you get b = 75. Plug b = 75 into any of the equations and you get a = 350. Therefore you need 350 batches of beverage a and 75 batches of beverage b.

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