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Question 390230: How would this problem be written as an equation:
Smith and Jones combined age is 91. Smith is twice as old as Jones was when Smith was as old as Jones is now.
I solved the question but do not know how to write the equation!
Thanks in advance
Lou
Answer by J2R2R(94)   (Show Source):
You can put this solution on YOUR website! Smith and Jones combined age is 91. Smith is twice as old as Jones was when Smith was as old as Jones is now.
Smith is obviously the older and the age gap is d. Smith’s age is s and Jones’ age is j.
So we have two equations:
s + j = 91…………. (1)
s - d = j …………... (2)
Smith is twice as old as Jones was when Smith was as old as Jones is now, so reducing Smith’s age by d to make Smith what Jones’ age was gives us
s - 2d = j - d ……... (3)
Now j - d is what Jones’ age was d years ago which means that Smith’s age is now is twice that.
Therefore we use (3) to get
s = 2(s - 2d) …….... (4)
Rearranging (4): s = 2s - 4d gives 4d = s or d = s/4
Substituting this into (2): s - s/4 = j gives 3s/4 = j
Now substituting this into (1) gives s + 3s/4 = 91
7s/4 = 91; s/4 = 13; s = 52; j = 39.
So, Smith is 52 and Jones is 39; 13 years ago when Smith was 39 Jones was 26.
Check the details:
52 + 39 = 91
When Smith was 39, Jones was 26; Smith is now 2 times 26 = 52.
I hope this helps.
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