Cryptic Algebra V.1

In order to narrow the number of possibilities for each of the letters, we have to deduce it by looking at the conditions. Since TWO X TWO is the same as TWO squared , and the letter T can be found at the start of each word, which we can easily deduce where TWO ranges from.

Let's try substituting the word TWO with 142 such that,

$142^2$ = 20164

We can see that the letter T on THREE does not match the number of letter T on TWO , it means that the word TWO is less than 142 and the product THREE is less than 20,000. We can also infer that T = 1 , therefore W and O is not equal to 1 . Also, O must not be 0 and 5 because that will contradict the letter E on the product. The tens digit and ones digit must be different, so 122 and 133 can not be the solution. There are only 19 numbers that can be substituted to the word TWO . By listing all the remaining numbers.

10404 =102 X 102

10609 =103 X 103

10816 =104 X 104

11236 =106 X 106

11449 =107 X 107

11664 =108 X 108

11881 =109 X 109

15129 =123 X 123

15376 =124 X 124

15876 =126 X 126

16129 =127 X 127

16384 =128 X 128

16641 =129 X 129

17424 =132 X 132

17956 =134 X 134

18496 =136 X 136

18769 =137 X 137

19044 =138 X 138

19321 =139 X 139

The only number when squared that has the 2 E's or 2 same digits at the end is 19044 which is 138 X 138 .

Therefore, T=1, W=3, O=8, H=9, R=0, E=4

Then, we can substitute these numbers to the problem,

TWEET $\rightarrow$ 13441

WORTH $\rightarrow$ 38019

OR $\rightarrow$ 60

Applying the operation

$\frac{13441 +38019}{60}$ = $\boxed{643.25}$