Question

Lucy works for a company that manufactures liquid dyes for fabric. She currently wants to mix up some 23%-concentrated teal dye. She has 16 gallons of 15%-concentrated teal dye, as well as plenty of 25%-concentrated teal dye. How many gallons of the 25%-concentrated teal dye will Lucy need to add to the 15%-concentrated teal dye to make a batch with a concentration of 23%? _____ gallons

Answer 1

Answer: 64 gallons

Step-by-step explanation:

Let he mixed x gallons of 25%-concentrated teal dye with 16 gallon of 15%-concentrated teal dye to make 23%-concentrated teal dye.

Thus, the total quantity of the resultant dye = (16+x) gallon

Also,

The concentration of 25%-concentrated teal dye + the concentration of 15%-concentrated teal dye = The concentration of 23%-concentrated teal dye.

⇒ 25 % of x + 15 % of 16 = 23 % ( x + 16 )

⇒ 25 of x + 15 of 16 = 23  ( x + 16 )

⇒ 25 x + 15 × 16 = 23 x +  23 × 16

⇒ 25 x + 240 =  23 x + 368

⇒ 25 x + 240 - 23 x = 368

⇒ 2 x  = 368 - 240

⇒ 2 x  = 128

⇒ x = 64

Hence, the quantity of 25%-concentrated teal dye = 64 gallons