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