[spirochete]

A 40% solution of acid has a density of 1.3 g/mL and a 60% solution has a density of 1.55 g/mL.  What's the density of a 50% solution?  Approximate the relationship as linear.

I already know the answer is 1.4.  Hopefully that will get me some sympathy and somebody can just show me how to do this.

[vhpk]

A 40% solution of acid has a density of 1.3 g/mL and a 60% solution has a density of 1.55 g/mL.  What's the density of a 50% solution?  Approximate the relationship as linear.

I already know the answer is 1.4.  Hopefully that will get me some sympathy and somebody can just show me how to do this.

Firstly, you need to calculate the rate of volume between 2 solutions of 40% and 60% to give the solution of 50%. The result I get is 1:1
Assume, the volume of each solution is 1ml. I'll introduce a method which we always use for calculation of C%, CM, density when 2 solutions are mixed together.
1(ml) A with d = 1,55g/ml                        d - 1,3
                                        C with d
1ml B with d = 1,3g/ml                            1,55 - d
Now we have the rate:
1/1 = (d-1,3)/(1,55-d)
=> d = 1,425g/ml

[enahs]

Just solve a linear regression for the slope and y-intercept of the line, then plug back into X, it is much easier.

I.E., use those two points and solve for the slope and y-intercept. Any calculator now-a-days can do it.

vhpk's method is more scientific looking, but whatever works for you do it.

[spirochete]

I should have mentioned in the OP I was looking for the easiest way to do this without a calculator, since the question is from a practice test for a standardized test.

[enahs]

Well, I mean, calculating the slope from two points and the y-intercept is pretty trivial . That is all vhpk's method did essentially, only his was based around the science and not just pure math.