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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

Dave is twice as old as Rick. 10 years ago the sum of their age was 40. how old are they now How do you set this inequality up

x-10 for rick age

2(x-10) for daves

### 4 Answers by Expert Tutors

Erik S. | Math is the best subject in which I have ever tutoredMath is the best subject in which I have...
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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.

Virginia K. | Elementary thru Highschool with emphasis on MathElementary thru Highschool with emphasis...
4.9 4.9 (404 lesson ratings) (404)
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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!

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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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.

Maurizio T. | Statistics Ph.D and CFA charterholder with a true passion to teach.Statistics Ph.D and CFA charterholder wi...
5.0 5.0 (334 lesson ratings) (334)
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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.