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?

Click here to see ALL problems on Age Word Problems

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.