
John M. answered 03/30/15
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Analytical assistance -- Writing, Math, and more
Emily, the keys are (1) translating the words into algebra and (2) remembering that everyone ages at the same rate.
So if we define F=Grandfather's age now and D=Granddaughter's age now, the first sentence translates as
F is 5 times as old as D. The "is" is the equal sign, and times means multiplication, so it becomes
F=5xD
In six years, Grandfather's age is F+6, and Granddaughter's age is D+6, so the second sentence translates as
(F+6) will be 4 times as old as (D+6). "Will be" is just the equal sign ("is" is a be verb too), so it becomes
(F+6)=4x(D+6)
So your two equations, two unknowns are F=5D & (F+6)=4(D+6)
Starting with the second equation, distribute the 4 across the parentheses so
F+6 = 4D + 24
Then use the 1st equation to substitute 5D for F
5D + 6 = 4D + 24
Subtract 4D from both sides of the equation
5D - 4D + 6 = 4D - 4D + 24
D + 6 = 24
Subtract 6 from both sides
D + 6 - 6 = 24 - 6
D = 18
Substitute D=18 back into F=5D
F = 5D = 5x(18)
F=90
So the Granddaughter is now 18 and the Grandfather is now 90. Checking our work, in six years
the Granddaughter will be 24 and the Grandfather will be 96. 24 time 4 = 96, check.
I hope this helps. John