word problem

Question

A tea distributor needs to mix a(n) Terraza tea blend that normally sells for $2.89 per pound with a Gazebo tea blend that normally sells for $2.71 per pound to create 52 pounds of a tea that can sell for $2.77 per pound. How many pounds of each kind of tea blend should they mix?

 

Answer: They must mix
_____pounds of the Terraza Blend
_____pounds of the Gazebo Blend.
Round your answers to the nearest pound.

Answer 1

Let T = lbs of Terraza and let G = lbs of Gazebo

 

Tx2.89 + Gx2.71 = 52x2.77

T + G = 52 and T = 52-G (substitute in equation 1)

 

(2.89)(52-G) + 2.71G = 144.04

150.28 - 2.89G + 2.71G = 144.04

0.18G = 6.28

G = 34.89 lbs of Gazebo = 35 lbs Gazebo

T = 52 - 34.89 = 17.11 lbs of Terraza = 17 lbs Terraza

 

OR you can do this by a method known as alliteration:

HAVE..........WANT..........NEED

2.89................................6...

..................2.77...................

2.71...............................12....

 

So, you need to use 6 parts of the 2.89/lb and 12 parts of the 2.71/lb for a total of 18 parts

Since you want 52 pounds total, 18 parts thus is equal to 52 lbs and 1 part = 52/18 = 2.89 lbs

2.89 lbs x 6 parts = 17 lbs of Terraza

2.89 lbs x 12 parts = 35 lbs of Gazebo