The height of two plants is in the ratio 7:9. The height of the taller plant is 26 cm more then the shorter one. What is their tot

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1. Given :-

   • The height of 2 plants is in the ratio 7:9
   • The height of the taller plant is 26cm more than the shorter one.

   Aim :-

   • To find the total height of both the plants

   Answer :-

   Ratio :-

   Ratio is the comparison between 2 or more quantities expressed in it’s simplest form.

   Here too the heights are expressed in it’s simplest form.

   Let the height of the shorter plant be y.

   According to the question, the height of the taller plant is then y + 26.

   Therefore,

   y : (y+26)  = 7:9

   [tex]\implies \sf \dfrac{y}{y+ 26} = \dfrac{7}{9}[/tex]

   By cross multiplication,

   [tex]\implies \sf 9(y) = 7(y+26)[/tex]

   [tex]\implies \sf 9y = 7y + 182[/tex]

   Transposing 7y,

   [tex]\implies \sf 9y – 7y = 182[/tex]

   [tex]\implies \sf 2y = 182[/tex]

   Transposing 2,

   [tex]\implies \sf y = \dfrac{182}{2}[/tex]

   Reducing to the lowest terms,

   [tex]\implies \sf y = 91[/tex]

   Now that we have the value of y, the heights of the plants will be :-

   • Smaller plant = 91cm
   • Taller plant = 91 + 26 ⇒ 117cm

   Verification :-

   Let us verify the answer by reducing 91:117 to the lowest terms.

   [tex]\implies \sf \dfrac{91}{117}[/tex]

   Both 91 and 117 are exactly divisible by 13. Hence, dividing both the numerator and the denominator by 13,

   [tex]\implies \sf \dfrac{91 \div 13}{117 \div 13}[/tex]

   [tex]\implies \sf \dfrac{7}{9}[/tex]

   The ratios are matching, hence the answer is correct.

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