I have a question regarding

Kaplan's GMAT Math Workbook. On page 252 (which is Chapter 5, 'Part Three: Question Type Review' on word problems) they give an explanation of a word problem that, to me at least, seems overly complicated. Here is their version:

"Example: Steve is now five times as old as Craig was 5 years ago. If the sum of Craig's and Steve's ages is 35, in how many years will Steve be twice as old as Craig?"

a) 2

b) 5

c) 10

d) 15

e) 25

Kaplan then goes on to explain how to unpack the question and set up an equation to solve. Here is how they set it up:

Let c = Craig's current age

Let s = Steve's current age

(first part of problem) => s=5(c-5)

(second part of problem) => c+s=35

(this is where they seem to complicate matters to me):

c+s=35

c=35-s

s=5(c-5)

s=5(35-s-5)

s=5(30-s)

s=150-5s

6s=150

s=25

(therefore) c=10

(now they complete the final part of the problem and solve for what the problem asks):

25+x=2(10+x)

25+x=20+2x

(answer) x=5

So, as a non-quant, this is what I would like the quants on the forum to answer for me. Why didn't they just do it this way and eliminate a significant step?

s=Steve's age now

c=Craig's age now

c+s=35

s=5(c-5)

c+5(c-5)=35

c+5c-25=35

6c=60

c=10

(therefore) s=25

25+x=2(10+x)

x=5

You get the same result but you don't have to do the whole {c+s=35; c=35-s; s=5(c-5); s=5(35-s-5)} mumbo-jumbo. (mumbo-jumbo is NOT going to appear on the GMAT for all you non-native speakers)

What gives?

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