CPhill

Thanks, Isabelle and EP.......here's one more way of looking at it

Each side of the smaller triangle is 9/10 of its respective side in the larger triangle

So   47 (9/10)  = 42.3m

Good to see you, Piperson......wecome back....!!!!

4/9   = 36/A    where A is the number of adult meals......cross-multiply

4A  =  36 * 9

4A  =  324     divide both sides by 4

A = 81

Total number of meals sold =  36 + 81 =    117

x^3 - x^2 =55   subtract 55 from both sides

x^3 - x^2  - 55   = 0

This would be difficult to solve algeraically.....here are the solutions :

http://www.wolframalpha.com/input/?i=x%5E3+-+x%5E2++-+55+++%3D+0

x ≈ 4.1672

x ≈ -1.5836 - 3.2696 i

x ≈ -1.5836 + 3.2696 i

log₁₀(10^2)=2

log₁₀ 100 = 2     in exponential form, if we have  log_a b = m. we can write   a^m  = b....so

10^2   = 100

[m - 3] / 4   = [m + 1 ] / 3        cross-multiply

3 [ m - 3 ]  = 4 [ m + 1]       simplify

3m - 9    =  4m + 4     add 9 to both sides, subtract 4m from both sides

-1m   =  13          divide both sides by -1

m = -13

x log (5) - y log (2)     we can write

log (5)^x - log (2)^y    and this simpilfies to

log  (5^x / 2^y)

Thanks, HSC.....

Recursive rule

a_n+1  = 4 * a_n

Explicit rule

a_n   =  2 ^{(2n - 1)}

4th term   =  2 ^{(2n - 1)}   =   2 ^{(2*4 - 1)}   = 2 ⁽⁷⁾   =  128    =   4 * 32

5th term  =  4 * 128 =  512

6th term = 4 * 512   =  2048

a_{n + 1}  = 3*a_n    and the nth term is given by:

5 * 3 ^{(n - 1)}   so the 13th term is    5 * 3 ^{(13 - 1)}   = 5 * 3 ¹²  =  2,657,205