The sum of 3 times Darlene's age and 7 times Sharon's is 173. Darlene is 2 years less than twice as old as Sharon is. How do you find each of their ages?

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Answer 1 · 2015-09-06T21:30:55

With the question as given Darlene is #13 10/13# and Sharon is #25 7/13#.

If the #173# is a typo for #163#, then Darlene is #13# and Sharon is #24#.

Let #d# be Darlene's age and #s# be Sharons's age.

We are given:

#3d+7s = 173#

#d = 2s-2#

Substitute this second equation into the first to get an equation in #s#:

#173 = 3d + 7s = 3(2s-2) + 7s = 6s - 6 + 7s = 13s - 6#

Add #6# to both ends to get: #13s = 173+6 = 179#

Divide both ends by #13# to get: #s = 179/13 = 13 10/13#

Hence #d = 2s-2 = 2*179/13 - 2 = 358/13 - 26/13 = 332/13 = 25 7/13#

I suspect the #173# in the question should be #163#, which would yield: #s = 13# and #d = 24#.