Question

The sum of two numbers is 25. If the first number is decreased by 5 the second is increased by 1. the product of the new no. s is 108 find the original numbers.
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Answer 1

Answer:

let x be first number and y be second number.

by given condition,

x+y=25

.•.x=25-y------------------[1]

by second condition,

(x-5)(y+1)=108

(25-y-5)(y+1)=108------------------[from 1]

(20-y)(y+1)=108

20y+ 20 -y^2 -y=108

-y^2+19y+20-108=0

y^2-19y+88=0-----------[multiplying by -1]

y^2-11y-8y+88=0

y(y-11)-8(y-11)=0

(y-8)(y-11)=0

y-8=0. or. y-11=0

y=8. or. y=11

put y=8 in [1],

x=25-8

x=17

put y=11 in [1]

x=25-11

x=14

.•.x=17. and. y=8

or

.•.x=14. and. y=11