Sister age ratio

Three sisters have birthdays today, and their ages are in the ratio of 2:3:4. In two years, their ages will be in the ratio of 5:7:9. Find what their ages will be in four years.

Final Answer:

p = 3:4:5

Step-by-step explanation:

a:b:c = 2:3:4 (a+2):(b+2):(c+2) = 5:7:9  a=2⋅ x b=3⋅ x c = 4⋅ x  a+2 = 5⋅ y b+2 = 7⋅ y  2x+2=5⋅ y 3x+2=7⋅ y  2⋅ x+2=5⋅ y 3⋅ x+2=7⋅ y  2x−5y=−2 3x−7y=−2  Pivot:Row1↔Row2  Row2−32​⋅ Row1→Row2 −0.33y=−0.67  y=−0.33333333−0.66666667​=2 x=3−2+7y​=3−2+7⋅ 2​=4  x=4 y=2  a=2⋅ x=2⋅ 4=8 b=3⋅ x=3⋅ 4=12 c=4⋅ x=4⋅ 4=16  p = (a+4):(b+4):(c+4)  p = (8+4):(12+4):(16+4) p = 12:16:20 p=3:4:5

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