A grandfather is 5 times as old as his granddaugter. In 6 years, he will be 4 times as old as his granddaughter will be find the age of each person now

Question

this confuses me If you could solve it and show me how to do it as simply as you can then thanks

Answer 1

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