A chemist wants to make 50ml of 17% acid solution by mixing a 13% acid solution. How many milliliters of each solution should the chemist use?

Solution:
1. Let x be the volume (in ml) of the 13% acid solution.
2. Let y be the volume (in ml) of pure acid (100% acid).

Given:
- Total volume x + y = 50 ml
- Desired concentration: 17%

3. Set up the equation for the acid content:
0.13x + y = 0.17 \times 50

4. Simplify:
0.13x + y = 8.5

5. Solve the system of equations:
a) x + y = 50
b) 0.13x + y = 8.5

6. Subtract equation (b) from equation (a):
(x + y) - (0.13x + y) = 50 - 8.5
x - 0.13x = 41.5
0.87x = 41.5
x = \frac{41.5}{0.87}
x \approx 47.7

7. Substitute x \approx 47.7 back into x + y = 50:
47.7 + y = 50
y = 50 - 47.7
y \approx 2.3

So, the chemist should use approximately 47.7 ml of the 13% acid solution and 2.3 ml of pure acid.