Question

eli wants to combine 0.5 gallons of a 10% acetic acid solution with a 35% solution to make a 15% acetic acid solution. he needs to determine how many gallons of 35% solution are needed. eli decides to let v represent the volume of 35% solution and makes a table to help solve the problem. help eli by completing the table. drag each tile to the correct cell in the table. v 0.15(v + 0.5) 0.35v (0.10)(0.5) 0.5 0.15 0.10 v + 0.5 0.35

Explanation:

Step1: Analyze the 10% acid solution

The amount of 10% acid solution is given as \(0.5\) gallons. The acid concentration is \(0.10\). The amount of acid is calculated as \((0.10)(0.5)\) (using the formula \(Amount\ of\ Acid=Acid\ Concentration\times Amount\ of\ Solution\)).

Step2: Analyze the 35% acid solution

The volume of the 35% acid solution is represented by \(v\). The acid concentration is \(0.35\). The amount of acid is \(0.35v\) (using the formula \(Amount\ of\ Acid = Acid\ Concentration\times Amount\ of\ Solution\)).

Step3: Analyze the mixture

The total volume of the mixture is \(v + 0.5\) (sum of the volumes of the two solutions). The acid concentration of the mixture is \(0.15\). The amount of acid in the mixture is \(0.15(v + 0.5)\) (using the formula \(Amount\ of\ Acid=Acid\ Concentration\times Amount\ of\ Solution\)).

Answer:

	Amount of Solution	Acid Concentration	Amount of Acid
35% Acid	\(v\)	\(0.35\)	\(0.35v\)
Mixture	\(v + 0.5\)	\(0.15\)	\(0.15(v + 0.5)\)