Question

latrell works for a company that manufactures liquid dyes for clothing. he currently wants to mix up some 38%-concentrated pink dye. he has 54 liters of 26%-concentrated pink dye, as well as plenty of 46%-concentrated pink dye. how many liters of the 46%-concentrated pink dye will latrell need to add to the 26%-concentrated pink dye to make a batch with a concentration of 38%?
write your answer as a whole number or as a decimal rounded to the nearest tenth.
liters

Explanation:

Step1: Set up the equation

Let \(x\) be the liters of \(46\%\) - concentrated pink dye.
The amount of pure dye in \(26\%\) - concentrated dye is \(0.26\times54\).
The amount of pure dye in \(46\%\) - concentrated dye is \(0.46x\).
The total volume of the mixture is \(54 + x\), and the amount of pure dye in the mixture is \(0.38(54 + x)\).
So, \(0.26\times54+0.46x=0.38(54 + x)\).

Step2: Expand and simplify the equation

First, expand both sides:
\(14.04+0.46x = 20.52+0.38x\).
Subtract \(0.38x\) from both sides: \(14.04 + 0.46x-0.38x=20.52+0.38x - 0.38x\), which gives \(14.04+0.08x=20.52\).
Then subtract \(14.04\) from both sides: \(0.08x=20.52 - 14.04\).
So, \(0.08x=6.48\).

Step3: Solve for \(x\)

Divide both sides by \(0.08\): \(x=\frac{6.48}{0.08}=81\).

Answer:

\(81\)