IXL - Weighted averages: word problems (Geometry practice)

A teaching assistant at a university needs 28% acid solution for her class's lab experiment. There isn't any of this concentration in stock, but the lab has 50 liters of 22% acid solution, as well as a lot of 32% acid solution. How much of the 32% acid solution should the teaching assistant add to the 22% acid solution to obtain a solution with the desired concentration?

Write your answer as a whole number or as a decimal rounded to the nearest tenth.

liters

ref_doc_title.

Learn with an example

question

A fuel producer is formulating a fuel mixture that contains 75% ethanol. To make this fuel, they will take 460 gallons of 80% ethanol fuel and add some 55% ethanol fuel. How much of the 55% ethanol fuel should be added?

Write your answer as a whole number or as a decimal rounded to the nearest tenth.

gallons

solution

Step 1: Define a variable and make a table.

Let x represent the quantity of 55% fuel. Now make a table.

Start by filling in the first two columns with what you know.

	Concentration	Amount of fuel (gallons)	Amount of ethanol (gallons)
80% fuel	0.8	460
55% fuel	0.55	x
75% fuel	0.75

Next, finish filling in the second column. Since there are 460 gallons of 80% fuel and x gallons of 55% fuel, there are a total of

460

gallons of 75% fuel. Fill in

460

	Concentration	Amount of fuel (gallons)	Amount of ethanol (gallons)
80% fuel	0.8	460
55% fuel	0.55	x
75% fuel	0.75	460 + x

Finally, multiply across to fill in the third column.

	Concentration	Amount of fuel (gallons)	Amount of ethanol (gallons)
80% fuel	0.8	460	0.8 ( 460 )
55% fuel	0.55	x	0.55 x
75% fuel	0.75	460 + x	0.75 ( 460 + x )

Step 2: Write an equation and solve.

Using the information in the table, write an equation.

0.8 ( 460 )	+	0.55 x	=	0.75 ( 460 + x )

amount of ethanol in 80% fuel		amount of ethanol in 55% fuel		amount of ethanol in 75% fuel

Solve the equation.

0.8

(

460

)

0.55

0.75

(

460

)

368

0.55

Multiply

345

0.75

Multiply

368

–

0.2

Subtract

0.75

from both sides

345

Subtract

0.75

from both sides

–

0.2

Subtract 368 from both sides

–

Subtract 368 from both sides

Divide both sides by

–

0.2

115

Divide both sides by

–

0.2

To make 75% ethanol fuel, 115 gallons of the 55% ethanol fuel should be added.

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