Question

Find two numbers so that their sum, difference and product form a ratio of 6:4:15
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Answer 1

Answer:

the solution is (x,y) = (15,3)

Step-by-step explanation:

let x and y be the 2 no.s

given that their sum, difference and product ration = 6:4:15

let m be the proportionality constant

=> x+y = 6m ------------ (1)

    x-y = 4m  ------------ (2)

and xy = 15m  ------------ (3)

(1) + (2) => x+y + x-y = 6m+4m

           => 2x = 10m

           => x = 5m

substitute the value of x = 5m in (3)

=> (5m)y = 15m

=> y = 15m/5m

=> y = 3

(1)-(2) => x+y - (x-y) = 6m-4m

         => x+y-x+y = 2m

         => 2y = 2m

         => y = m

         => m=3

substitute the value of m=3 in x = 5m

=> x = 5(3)

=> x = 15

=> the solution is (x,y) = (15,3)

verification:

x+y = 15+3 = 18

x-y = 15-3 = 12

xy = 15*3 = 45

so, (x+y) : (x-y) : (xy)

=>    18 : 12 : 45

=>      6: 4 : 15

verified