How many gallons of 25% concentrated due will Lucy need to add to the 15% concentrated dye to make a batch with a concentration of 23%?

Complete question is;

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%?

64 gallons

Explanation:

We are given;

Quantity of 15%-concentrated teal dye = 16 gallons

Let the number of gallons of 25%-concentrated teal dye needed to add to make the batch with a concentration of 23% be represented as x.

Thus;

(15% × 16) + (25%)x = 23%(16 + x)

Multiply each term by 100 to give;

(15 × 16) + 25x = 23(16 + x)

240 + 25x = 368 + 23x

Rearranging, we have;

25x - 23x = 368 - 240

2x = 128

x = 128/2

x = 64

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