QNo1: Solve each of the follwing Simultaneous Equations step wisewith variables.

Question

QNo1: Solve each of the follwing Simultaneous Equations step wisewith variables. a) A farmer keeps hens and rabbits on his farm.One day hecounted a total of 70 heads and 196 legs. How many more hens thanrabbits does he have? b) The sum of the digits of a two-digit number is 12, and theunits digit is twice the tens digit. Find the nuimber? Hint:- Answer Should be (a) 14 more hens  (b)48 a) A farmer keeps hens and rabbits on his farm.One day hecounted a total of 70 heads and 196 legs. How many more hens thanrabbits does he have? b) The sum of the digits of a two-digit number is 12, and theunits digit is twice the tens digit. Find the nuimber? Hint:- Answer Should be (a) 14 more hens  (b)48

Explanation / Answer

(a) let hens=H rabbits = R since total head is 70, H+R=70                (eq1) total legs is 196, 2H+4R=196          (eq2) multiply the eq1 and substract by eq2 therefore, R=28               H=42 therefor 14 more hens than rabbits . (b) let two digit No is: x y, y-units digit x-tens digit sum of two digit=12, x+y=12                                (eq3) units digit is twice the tens digit y=2x                                     (eq4) therefore 3x=12, x=4 y=8 therefore the number is, 48

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