Alan

I think the question is:

Mary is 24.  She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?

Mary = 24

x years ago:   Mary - x = Ann  so 24 - x = Ann

           Also:   Mary = 2(Ann - x)

              So:   24 = 2(24 - x - x)

                  :   24 = 48 - 4x

                  :   x = 6

 Ann = 24 - x = 24 - 6, so Ann = 18 

Here's a graph of the standardised normal cumulative probability curve to illustrate the relationship between the middle 75% and the values ±1.15.

Here's my reasoning:

If you are on pedestal 1 the probability of your friend being next to you is 1/23

Same if you are on pedestal 24

If you are on any of the other 22 pedestals the probability is 2/23

Hence the overall weighted probability is (2/24)*(1/23) + (22/24)*(2/23) 

$$\left({\frac{{\mathtt{2}}}{{\mathtt{24}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{23}}}}\right){\mathtt{\,\small\textbf+\,}}\left({\frac{{\mathtt{22}}}{{\mathtt{24}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{2}}}{{\mathtt{23}}}}\right) = {\frac{{\mathtt{1}}}{{\mathtt{12}}}} = {\mathtt{0.083\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

The middle 75% means the upper and lower limits are at the points 87.5% and 12.5% respectively (i.e. 25% in total beyond these limits).  

Never mind; what's a factor of 100 among friends!

The mass at time 0 is found by replacing t by zero in 10e^-0.013t

Since e⁰ = 1 this means the mass at time zero is just 10 kg.

Replace t by 42 to find the mass after 42 days (assuming that the decay constant has units of days^-1)

$${\mathtt{massafter42days}} = {\mathtt{10}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\mathtt{0.013}}{\mathtt{\,\times\,}}{\mathtt{42}}\right)} \Rightarrow {\mathtt{massafter42days}} = {\mathtt{5.792\: \!622\: \!313\: \!807\: \!82}}$$

So approximately 5.79kg remain after 42 days.

Here's another inequality I want to turn into equalities.

Separately find the extreme values.

1. -8 = 4 - 2x₁

Add 8 to both sides:  0 = 12 - 2x₁

Add 2x₁ to both sides 2x₁ = 12

Divide by 2:  x₁ = 6 

2. 4 - 2x₂ = -5

Add 5 to both sides: 9 - 2x₂ = 0

Add 2x₂ to both sides: 9 = 2x₂

Divide by 2 to get x₂ = 4.5

The extreme values are 4.5 and 6. The only point to beware of here is that x can equal the second (lower) limit, but is strictly less than the first (upper) limit. So  4.5 ≤ x < 6 

I don't like inequalities!  I try to turn them into equalities.  We can do this here by separately finding the two extremes:

1. 0.39m₁ + 2600 = 6890

Subtract 2600 from both sides:  0.39m₁ = 4290

Divide both sides by 0.39:  m₁ = 4290/0.39 = 11000

2. 0.39m₂ + 2600 = 8840

Subtract 2600:  0.39m₂ = 6240

Divide by 0.39: m₂ = 6240/0.39 = 16000

Hence the range is between 11000 and 16000 miles.