July 2026
Problem of the Month

Temperature Scales

Melvin and Rachel have created new thermometer scales.
On the Melvin scale, water freezes at 5° M and boils at 45° M.
On the Rachel scale, water freezes at 50° R and boils at 110° R.

What temperature on the Melvin scale is 74° R?

Solution to the Problem:

M = 21°.

You know the following:

C	M	R
0	5	50
100	45	110

Think of R as a function of M.
Determine the slope: (ΔR / ΔM) = (110 - 50) / (45 - 5) = 60/40 = 3/2

Then you can write:
R - 50 = 1.5 (M - 5)
R - 50 = 1.5M - 7.5)
2R - 100 = 3M - 15)

Sub R = 74 to get:
148 - 100 = 3M - 15
3M = 63
M = 21

Correctly solved by:

1. Davit Banana	Istanbul, Turkey
2. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
3. Colin (Yowie) Bowey	Beechworth, Victoria, Australia

Send any comments or questions to: David Pleacher