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Representing linear equations for a word problem

Question 35St...

Question

Question 35

State whether the statement is true (T) or false (F).

In a 2-digit number, the unit's place digit is x. If the sum of the digits be 9, then the number is (10x-9).

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Solution

False
Given, unit's digits=x
and sum of digits=9
$∴$ Ten's digit =9-x
Hence, the number=10(9-x)+x=90-10x+x=90-9x

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Question 35

State whether the statement is true (T) or false (F).

In a 2-digit number, the unit's place digit is x. If the sum of the digits be 9, then the number is (10x-9).

The sum of digits of a two-digit number is 9. The digit at ten's place is twice the digit at unit's place. Then the number is

Q. A number consists of two digits whose sum is

9

27

is added to the number, its digits are interchanged. Are the given steps to find the number true?
Step

1

: Let the unit's digit be x
Step

2

: Then, ten's digit

= (9 - x)

∴

= 10 \times (9 - x) + x \Rightarrow 90 - 10 x + x = (90 - 9 x)

3

27

90 - 9 x

117 - 9 x

4

: Number with digits interchanged is

10 x + (9 - x) = 9 x + 9

5

117 - 9 x = 9 x + 9

6

: Therefore unit's digit

= 6

and ten's digit

= 3

7

: Hence the number

= 36

.

Question 84

In the following question, state whether the given statement is true (T) or false (F).
If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 9.

Q. The sum of the digits of a two-digit number is 9 less then the number. Which of the following digits is at unit's place of the number ?

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Representing linear equations for a word problem

Standard VIII Mathematics

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