Alan

As follows:

Note that \(x^{1/3}=\frac{x}{x^{2/3}}=\sqrt[3]x\)  so let \(u=x^{1/3}\) and we have \(4u-2u=7+u\)

Simplifying, we get \(u=7\)  so \(x=u^3=7^3=343\)

Sorry, I shoud have provided more verbal explanation.

1st step: Invert the fraction and set 'a' to be the largest integer less than or equal to the result.

2nd step.  Subtract 'a' from the inverted fraction.  If this isn't zero

3rd step:   Repeat the first two steps with the fraction left over from step 2, to get the next constant until step 2 results in zero. 

Like so

One way:  3 + 1/3

Another way:  10/3

I think the denominator on the LHS is sec²(x), not sec(2x), so we have:

Use Pascals Triangle to expand (x+4y)^5

I'll leave you to simplify further.

T = number of T-shirts, P = number of pants

2T + 4P = 67.9                    (1)

5T + 9P = 160.25                (2)

Multiply (1) by 5 and (2) by 2

10T + 20P = 5*67.9           (3)

10T + 18P = 2*160.25       (4)

Subtract (4) FROM (3)

2P = 5*67.9 - 2*160.25

Divide by 2

P = 2.5*67.9 - 160.25

Hence  P = 9.5

Substitute this back into (1) or (2) and rearrange to find T.

This might help you understand the result given by Max:

I guess the picture should look something like this (not to scale!!):

where  \(\frac{AB}{100}=\frac{42}{22}\)