They started equal. Martha spent $21 more than Mary ($36 vs $15), so after spending Mary has $21 more than Martha. Mary now = 2 units, Martha now = 1 unit, so that extra unit is the $21.

Martha now1Mary now11extra Martha spent = 36 − 15 = $21

Plain numbers are given; italic underlined numbers are worked out.

  1. Extra spent by Martha → $36 − $15 = $21
  2. Mary − Martha now = 1 unit → $21 (so Martha now = $21, Mary now = $42)
  3. Mary at first → $42 + $15 = $57
  4. Both started equal → total = 2 × $57 = $114

They had $114 altogether at first.

Check: each $57; Mary $57−$15=$42, Martha $57−$36=$21, and $42 = 2 × $21. ✓

Alternative method (algebra)

  1. Let each start with $m. Mary: m − 15; Martha: m − 36.
  2. m − 15 = 2(m − 36) ⇒ m − 15 = 2m − 72 ⇒ m = 57.
  3. Altogether at first = 2 × 57 = $114.