James' Dad is 5 times older than James and James is twice as old as his sister Sara. In two years, the sum of their ages will be 58. How old is James now?
Representation: Let x = Sara's age
2x = James' age
10x = Their dad's age
Now In two years
Sara x x + 2
James 2x 2x + 2
Dad 10x 10x + 2
Equation: (x + 2) + (2x + 2) + (10x + 2) = 58
Solution: (x + 2) + (2x + 2) + (10x + 2) = 58
x + 2 + 2x + 2 + 10x + 2 = 58
13x + 6 = 58
13x = 52
----- ----- ⇒ x = 4; 2x = 8; 10x = 40
13 13
Answer: James is 8 years old.
Check: (x + 2) + (2x + 2) + (10x + 2) = 58
(4 + 2) + [2(4) + 2) + [10(4) + 2) = 58
6 + (8 + 2) + (40 + 2) = 58
6 + 10 + 42 = 58
58 = 58
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---Have a vigorous Friday---
