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Dave is twice as old as Rick 10 years ago the sum of their age was 40 how old are they now

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4 Answers

This word problem is talking about two guys, Dave and Rick, and their ages.  Since their ages are what we are looking for, we will assign two variables, D for Dave's age and R for Rick's age.  The equations are as follows:

D = 2*R                    Dave is now twice as old as Rick.

(D-10)+(R-10)=40      D-10 means how old Dave was 10 years ago, and R-10 means how old Rick was 10 years ago, and those past ages add up to 40.

 

Now that there is a D equation expressed in terms of R, we can plug it into the other equation so that the only variable left will be R:

[(2*R)-10]+(R-10)=40         substitution method

2R-10+R-10=40

3R-20=40

   +20=+20                 I am adding 20 on both sides of the equation so that one side can have 3R alone.

3R=60

3R/3=60/3

R=20

D=2*R=2*20=40

Therefore, Dave is now 40 years old, and Rick is now 20 years old.

If using "x" and "y" as your variables gets you confused maybe this will help:

D= Dave's current age

R= Rick's current age

Since Dave current age is twice Rick's current age than;

D=2R


D-10= Dave's age 10 years ago

R-10 = Rick's age 10 years ago

If the sum of their ages 10 years ago was 40 than:

(D-10) + (R-10) = 40

D-10+R-10 = 40

D+R-20 = 40

D+R =60

since you already know that D=2R , you can substitute

D+R = 60

2R +R =60

3R=60

R=20 which is Rick's current age

D=2R=40 which is Dave current age

Hope it helps!

If Rick is  x  years old, then Dave is  2x  years old.
10 years ago Rick was  (x - 10)  years old and Dave was  (2x - 10)  years old.
(x - 10) + (2x - 10) = 40
3x - 20 = 40
3x = 60
x = 20
Rick is 20  years old and Dave is 40.

Let x be Rick's age and y be Dave's age. Then we know that

1)  Dave is twice Rick's age, i.e., y =2x

2) 10 years ago, y-10 and x-10, were such that (y-10)+(x-10) =40 or,  x+y-20 = 40 i.e.  x+y=60

Thus you have two unknowns, x and y, and two equations:

y = 2x 

x+y=60.

Replace y by 2x in the second equation. This gives  x+2x = 60 or 3x=60 so x =20.

Finally y=2x = 40.

So, Dave is now 40 and Rick is 20. 

 

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