You are given the following equation
SIX + SIX + SIX + SIX + SIX + SIX = TRI
where each letter stands for a digit.
The value of SIX is ......
105
give a solution to it show how to
we need to know how you did it
TELL US
Six less than y
To find the value of the digit represented by SIX in the equation, we can go through the process of solving the equation step by step.
Let's assign a variable to each letter:
S = a
I = b
X = c
T = d
R = e
The equation becomes:
abc + abc + abc + abc + abc + abc = def
Since we have six instances of "SIX" on the left side of the equation, we can rewrite it as:
6abc = def
Now, let's examine the possible values of "def."
Since "def" is a three-digit number, it can range from 100 to 999.
Since "abc" is the same in all six occurrences of "SIX," "def" must be divisible by 6.
To find possible values of "def" that are divisible by 6, we can check if each number from 100 to 999 is divisible by 6.
After checking this, we can find that the possible values of "def" that are divisible by 6 are:
114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414, 420, 426, 432, 438, 444, 450, 456, 462, 468, 474, 480, 486, 492, 498, 504, 510, 516, 522, 528, 534, 540, 546, 552, 558, 564, 570, 576, 582, 588, 594, 600, 606, 612, 618, 624, 630, 636, 642, 648, 654, 660, 666, 672, 678, 684, 690, 696, 702, 708, 714, 720, 726, 732, 738, 744, 750, 756, 762, 768, 774, 780, 786, 792, 798, 804, 810, 816, 822, 828, 834, 840, 846, 852, 858, 864, 870, 876, 882, 888, 894, 900, 906, 912, 918, 924, 930, 936, 942, 948, 954, 960, 966, 972, 978, 984, 990, 996.
Now, we can break these numbers down into their prime factors and check if any of them have repeated digits. If a number has repeated digits, it becomes impossible for "def" to be represented by the sum of six digits.
After checking the prime factorization of the possible values of "def," we find that only two values stand out:
120 = 2^3 * 3 * 5
114 = 2 * 3 * 19
Since 120 has a repeated digit (the digit 0 appears twice) and 114 has no repeated digits, we can conclude that the value of SIX is 1.
Therefore, in the given equation, SIX = 1.