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Linear Equations in One Variable

Short Answer Type

111.

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112.

Solve for $straight x colon fraction numerator 7 straight x plus 14 over denominator 3 end fraction minus fraction numerator 17 minus 3 straight x over denominator 5 end fraction equals 6 straight x minus fraction numerator 4 straight x plus 2 over denominator 3 end fraction minus 5$

158 Views

113.

Solve for $space space space space straight x colon fraction numerator straight x minus left parenthesis 7 minus 8 straight x right parenthesis over denominator 9 straight x minus left parenthesis 3 plus 4 straight x right parenthesis end fraction equals 2 over 3$

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114.

Solve for $straight x colon fraction numerator left parenthesis 2 plus straight x right parenthesis left parenthesis 7 minus straight x right parenthesis over denominator left parenthesis 5 minus straight x right parenthesis left parenthesis 4 plus straight x right parenthesis end fraction equals 1$

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115.

A number is such that it is as much greater than 65 as it is less than 91. Find the number.

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116.

The numerator of a fraction is 2 less than the denominator. If 1 is added to its denominator, it becomes ½. Find the fraction.

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117.

After 24 years I shall be 3 times as old as I was 4 years ago. Find my present age.

157 Views

118.
If the sum of two numbers is 30 and their ratio is 2 : 3, then find the numbers.

Let one of the numbers be x.

∴ The other number = (30 - x)

   According to the condition, we have

                 $fraction numerator straight x over denominator left parenthesis 30 minus straight x right parenthesis end fraction equals 2 over 3$    [∴ The ratio number is 2:3]

$rightwards double arrow$                      3x = 2(30 - x)         [By cross multiplication]

$rightwards double arrow$                       3x = 60 - 2x

$rightwards double arrow$                  3x + 2x = 60

$rightwards double arrow$                      5x = 60

$rightwards double arrow$                        $straight x equals 60 over 5 equals 12$