Question

Read the following scenario:

A barista has to make sixty pounds of a special blend of coffee at Moonbucks, using Hazelnut Happiness beans and Pecan Delight beansIf there are fourteen fewer pounds of Hazelnut Happiness beans in the mixture than Pecan Delight beans, then how many pounds of each will she use?

If x represents the number of pounds of Pecan Delight coffee beans in the mixture, then which of the following equations could be set up in order to find the number of pounds of each variety of bean?

Possible Answers:
x+(14−x)=60

x+(x−60)=14

x+(x+60)=14

x+(x+14)=60

x+(x−14)=60

Answer 1

The amount of Hazelnut Happiness beans is 23 pounds and the Pecan Delight beans is 37 pounds.

x + (x - 14) = 60

Explanation:

There are 60 pounds of a special blend of coffee, having Hazelnut Happiness beans and Pecan Delight beans in the mixture.

If the amount of Hazelnut Happiness beans is assumed to be y pounds and that of Pecan Delight beans is x pounds, then we can write

x + y = 60 ............. (1)

Now, there are 14 pounds more Pecan Delight beans than Hazelnut Happiness beans in the mixture, then we can write

x = y + 14 .............. (2)

Now, solving equations (1) and (2) we get,

2y + 14 = 60

⇒ y = 23 pounds

And, from equation (1) we get, x = 60 - y = 37 pounds. (Answer)

Now, the equation in terms of x will be x + (x - 14) = 60 (Answer)