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

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

Tutors, please sign in to answer this question.

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

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!

* x* years old, then Dave is

10 years ago Rick was

(x - 10) + (2x - 10) = 40

3x - 20 = 40

3x = 60

x = 20

Rick is

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.

Terri M.

Test Prep Specialist with 2400 SAT, 35 ACT, 770 GMAT, and 177 LSAT

New York, NY

4.9
(219 ratings)

Dana R.

English/Math SAT PrepTutor with PhD

Lynbrook, NY

4.8
(85 ratings)

Justin H.

Math, Computer Science, and SAT Tutoring from a Google Engineer

New York, NY

5.0
(388 ratings)