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Linear Equations in One Variable

Short Answer Type

71.

5x - 3 = 3x + 7

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72.

4 over 3 x plus 5 over 2 equals negative 3 over 2 plus x

177 Views

73.

Solve the following equation:

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133 Views

Long Answer Type

74.

The digits of a two digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, then we get 99. Find the original number.

278 Views

Short Answer Type

75.

Amino thinks of a number and subtracts 5/2 from it. She multiplies the results by 8. The result now obtained is 3 times the same number she thought of. What is the number?

178 Views

76.
A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Let positive number = 5x
The other number = x

∴
      On adding 21 to both number:

      We get (5x+21) and (x+21)

      According to the condition, we have

                                           $2 cross times left parenthesis x plus 21 right parenthesis equals 5 x plus 21$

or                                               2x + 42 = 5x +21

Transposing 42 to RHS, we have
                                             2x = 5x + 21 - 42
Transposing 5x to LHS, we have

                                           2x - 5x = -21

or                                             -3x = -21

   Dividing both sides by (-3), we have

                                             $fraction numerator negative 3 x over denominator negative 3 end fraction equals fraction numerator negative 21 over denominator negative 3 end fraction$

or                                               x = 7
and                                             5x = 5 $cross times$ 7 =35
   Thus, the required numbers are 7 and 35.

324 Views

Long Answer Type

77.

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

570 Views

Short Answer Type

78.

One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

464 Views

79.

Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one-third of his mother’s present age. What are their present ages?

388 Views

80.

There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11 : 4. At the rate Rs 100 per metre it will cost the village panchayat Rs 75000 to fence the plot. What are the dimensions of the plot?

278 Views