The sum of the digits of a two digit number is 10. If 18 be subtracted from it the digits i
the resulting number will be equal. The number is
Answers
Answer:
The answer is
Step-by-step explanation:
The sum of the digits of a two-digit number is 10. If 18 is subtracted from it, will the digits in the resulting number be equal?
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Let x = 10's digit of a two digit number
Let y = units digit
Let z = the resulting equal digits
:
Write an equation for each statement:
:
"the sum of a two digit number is 10."
x + y = 10
or
y = (10-x)
:
" if 18 be subtracted from it, the digits in the resulting number will be equal."
10x + y - 18 = 10z + z
10x + y = 11z + 18
:
Substitute (10-x) for y
10x + (10-x) = 11z + 18
10x - x = 11z + 18 - 10
9x = 11z + 8
:
The single digit integer values for x and z are limited to x=7 and z=5 in this equation:
x = 7, y = 3, z = 5
:
The number is 73
:
Check in the statement:
"if 18 be subtracted from it, the digits in the resulting number will be equal."
73 - 18 = 55
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The list of 2 digit numbers whose sum of digits is 10 is:
19 - When we substract 18: 19–18=01
91- When we substract 18: 91–18=73 ( Sum of digits 7+3=10)
28- When we substract 18: 28–18=10
82- When we substract 18: 82–18=64 (Sum of digits 6+4=10)
37- When we substract 18: 37–18=19 (Sum of digits 1+9=10)
73- When we substract 18: 73–18=55 (Sum of digits 5+5=10)
46- When we substract 18: 46–18=28 (Sum of digits 2+8=10)
64- When we substract 18: 64–18=46 (Sum of digits 4+6=10)
55- When we substract 18: 55–18=37(Sum of digits 5+5=10)
Observations:
Only in the case where 18 is substracted from 73 the resultant number 55 has equal digits.
In all other cases( except 19) when 18 is substracted, the resultant number also has sum of digits = 10 as shown above.
Let the number at unity be y and number at ten's place be x.
This means according to question we have,
x+y=10
y=10-x
Let z be a number which is equal in digit this means z=(x+y)/2 from this we conclude that z is 5.
2nd hint is if 18 is substracted from the digit in the resulting number will be equal,
10x+y-18=10z+z
10x+y-18=11(5)
10x+y=55+18
10x+10-x=73
9x=63
x=7 and y=3
So the number is 73
Hope you understood the solution.
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The sum of the digits of a 2-digit number is 10. If 18 is subtracted from it, the digits in the resulting number will be equal. What is the number?
No , that is not the case . Let us assume it is true , then the no.s
19
28
37
46
55
64
73
82
91
Shall satisfy the condition you mentioned . Each of the following no.s satisfy condition no. 1 that is ¬ if a no. XY is taken then X+Y =10 .
Now let us have a look at condition no. 2
XY-18 =ZZ . Now we subtract 18 from each of the above no.s
19-18 =01
28-18 =10
37-18= 19
46-18= 28
55-18 = 37
64-18= 46
73-18 = 55
And so on they don't give and integer with tens digit equal to ones digit . It gives us an arithmetic progression with a=1 and d=9.
No…Except for 73, it is not true for any other numbers
Take 19… 19–18 gives 1, there's only one digit
28… 28–18 gives 10.
37–18=19 and so on
91–18=73
Only one condition following the said scenario is 73. 73–18=55.
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Thus, 28 is the Two Digits Number in which 2+8 = 10 and Subtracting 18 from 28 i.e. 28–18=10.
Condition Satisfied in this case logically.
Let the digits be xy (x+y=10)
xy-18=10–18=-8