A beauty supply company has 5 gallons of 20% hydrogen peroxide solution on hand. The company also has a nearly limitless amount of a solution that contains 30% hydrogen
peroxide. How many gallons of the 30% hydrogen peroxide solution should the company add
to the 20% hydrogen peroxide solution to obtain a mixture that is 23% hydrogen peroxide?
Write your answer as a whole number or as a decimal rounded to the nearest tenth.

2.1 gallons

Step-by-step explanation:

Let V = volume of 20 % hydrogen peroxide = 5 gallons, V₁ = volume of 30 % hydrogen peroxide and V₃ = volume of 23 % hydrogen peroxide. So the final volume is V + V₁ = V₂

V₁ + 5 = V₂  (1)

Also, since quantity = concentration × volume,

Let Q = quantity of 20% volume hydrogen peroxide = 0.2V, Q₁ =  quantity of 20% volume hydrogen peroxide = 0.3V₁ and Q₂ = quantity of 23% volume hydrogen peroxide = 0.23V₂

So, 0.2V + 0.3V₁ = 0.23V₂

0.2 × 5 + 0.3V₁ = 0.23V₂

1 + 0.3V₁ = 0.23V₂

0.3V₁ - 0.23V₂ = -1  (2)

substituting equation (1) into (2), we have

0.3V₁ - 0.23(V₁ + 5) = -1

expanding the brackets, we have

0.3V₁ - 0.23V₁ + -0.23 × 5 = -1

0.07V₁ - 1.15 = -1

adding 1.15 to both sides, we have

0.07V₁ = -1 + 1.15

0.07V₁ = 0.15

dividing both sides by 0.07, we have

V₁ = 0.15/0.07

= 2.143 gallons

≅ 2.1 gallons to the nearest tenth

So, we need 2.1 gallons of 30 % hydrogen peroxide to obtain a mixture that is 23 % hydrogen peroxide.