SOLUTION: please help me solve this word problem: Jack is six years more than five times as old as Jill. if the sum of their ages is 78. how old is each?

Question 502219: please help me solve this word problem: Jack is six years more than five times as old as Jill. if the sum of their ages is 78. how old is each?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let Ja be Jack's present age and Ji be Jill's present age.
1) Ja + Ji = 78 "...the sum of their ages is 78."
2) Ja = 5Ji+6 "Jack is six years more than five times as old as Jill." Rewrite equation 1) as:
1a) Ja = 78-Ji and substitute for Ja in equation 2) to get:
2a) 78-Ji =5Ji+6 Solve for Ji. Add Ji to both sides
2b) 78 = 6Ji+6 Now subtract 6 from both sides.
2c) 72 = 6Ji Finally, divide both sides by 6.
2d) 12 = Ji Jill is 12 years old.
1b) Ja = 78=Ji
1c) Ja = 78-12
1d) Ja = 66 Jack is 66 years old.

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