We are given a mixture problem where a chemist mixes two detergent solutions — one at 10% concentration and another at 20% concentration — to make
500 mL of a
16% solution.
We need to find
how much of the 20% solution was used. Let’s call that amount
b.
---
Step 1: Define variables
As shown in the image:
- Let
a = amount (in mL) of 10% solution
- Let
b = amount (in mL) of 20% solution
We know two things:
1. The
total volume is 500 mL:
>
a + b = 500
2. The
total amount of detergent (pure substance) in the final solution is 16% of 500 mL:
> 0.16 × 500 =
80 mL of pure detergent
This comes from mixing:
- 10% of a →
0.1a
- 20% of b →
0.2b
So:
>
0.1a + 0.2b = 80
---
Step 2: Solve the system of equations
We have:
> (1) a + b = 500
> (2) 0.1a + 0.2b = 80
Let’s solve equation (1) for
a:
> a = 500 - b
Now substitute into equation (2):
> 0.1(500 - b) + 0.2b = 80
> 50 - 0.1b + 0.2b = 80
> 50 + 0.1b = 80
Subtract 50 from both sides:
> 0.1b = 30
Divide both sides by 0.1:
>
b = 300
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Step 3: Interpret the answer
Since
b = 300, this means the chemist used
300 mL of the 20% detergent solution.
To double-check, we can find
a:
> a = 500 - b = 500 - 300 =
200 mL of 10% solution
Check detergent total:
> 0.1 × 200 = 20 mL
> 0.2 × 300 = 60 mL
> Total = 20 + 60 =
80 mL → which is 16% of 500 mL ✔️
---
✔ Final Answer:
The chemist used 300 milliliters of the 20% detergent solution.
Parent Tip: Review the logic above to help your child master the concept of mixture word problems worksheet.
