**Question**

**Thinking / Planning**

Noting that Sarah spent all
her money in both scenarios and that 22´(18´something) = 18´(22´something) , I am going to first guess that Sarah takes 18 days and 22 days to spend all her money
in the 1

^{st}scenario and the 2^{nd}scenario respectively. [ Heuristics: H07. Use guess and check & H08. Make suppositions ] Then I try to adjust my educated guess.
Johari spent more money in the second scenario. The difference in his spending
among the two cases is 6, so we need

10´(number of days_{2}) – 12´(number of days

_{1}) = 6

**Solution**

If Sarah takes 18 days and 22 days respectively to spend
all her money, then

the difference in
Johari’s spending among the two cases is

10´(22) – 12´(18) =
4

´

^{3}/_{2}: 10´(33) – 12´(27) = 6**Ans (a):**Sarah has $22´27 = $594.

**Ans (b):**Johary has $(21+12´27) = $345.

**Commentary**

Anyway, a parent from a Facebook parent-support group posed this question asking for a simple solution without using
ratios. This question seems to be the
equivalent of a system of simultaneous equations in four variables. A few of us tried various methods to solve it,
but all were quite complicated. I knew
this can be solved using algebra, but struggled for some time to give a simple
solution.

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