Question

7×TUSHER=6×HERTUS
every alphabet here will be a number
For Further information:
T/U/S/H/E/R=0,1,2,3,4,5,6,7,8,9

SOLVE THE EQUATION ABOVE.

Answer 1

Answer on Question #83741 – Math – Combinatorics | Number Theory Question

$7 \times$ TUSHER $= 6 \times$ HERTUS

every alphabet here will be a number

For Further information:

T/U/S/H/E/R=0,1,2,3,4,5,6,7,8,9

SOLVE THE EQUATION ABOVE.

Solution

Denote $HER = a$, $TUS = b$. These are two 3-digit numbers.

Then

$$TUSHER = 1000b + a, \quad HERTUS = 1000a + b$$

We have

$$7(1000b + a) = 6(1000a + b)$$

from which

$$5993a = 6994b$$

or

$$461a = 538b$$

Since 461 and 538 are mutually prime numbers, $a$ should be divisible by 538. The only 3-digit number divisible by 538 is 538. So $a = 538$, from which $b = 461$.

Hence the answer is $H = 5, E = 3, R = 8, T = 4, U = 6, S = 1$.

Answer: $H = 5, E = 3, R = 8, T = 4, U = 6, S = 1$.

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