# Systems of Equations word problems

Hi,
I have three systems of equations word problems. Can you help me?

#1:
The sum of three numbers is 32. The largest if 4 times the smallest. The sum of the two smaller numbers is 8 less than the largest. What are the numbers?
I have tried to model this one.
I got:
_ + _ +_ = 32
Largest = 4S
Sum of the two smaller #S = L-8
Then I don't know what to do from there and got lost.

#2:
Dat is 10 years older than David. 38 years ago, he was twice as old as him. How old is David now?
This was one of my equations that I tried to come up with:
Y = D+10
Y = 2D + 38
Yeah, it doesn't really add up and so I don't really know what do with it.

#3:
Tiffany has 34 animals. She has 3 times as many birds as cats. She has 4 times as many cats as dogs. How many of each does she have?
For this one I got:
34 = B+C+D
Birds = 3C
Cats = 4D
Then I got put into a loop of plugging in values, so I need help building the equations with this one too.

Bystander
Homework Helper
Gold Member
Sum of the two smaller #S = L-8
Then I don't know what to do from there and got lost.
Try naming all three numbers and rewriting the equations.

Mark44
Mentor
Hi,
I have three systems of equations word problems. Can you help me?

#1:
The sum of three numbers is 32. The largest if 4 times the smallest. The sum of the two smaller numbers is 8 less than the largest. What are the numbers?
I have tried to model this one.
I got:
_ + _ +_ = 32
Largest = 4S
Sum of the two smaller #S = L-8
Then I don't know what to do from there and got lost.
As already mentioned, give a name to each variable, possibly like this:
Let L = the largest no.
Let S = the smallest no.
Let O = the other no. (the middle number).

Instead of "_ + _ +_ = 32" and "Sum of the two smaller #S = L-8", write equations using the variable names.
IsoXTargetz said:
#2:
Dat is 10 years older than David. 38 years ago, he was twice as old as him. How old is David now?
This was one of my equations that I tried to come up with:
Y = D+10
Y = 2D + 38
Which one is Dat? Which one is David? Define variable names so that their meanings are clear.
38 years ago, he was twice as old as him.
Huh? Who is he and who is him? This is about as unclear as it could possibly be. Surely this is not the original problem statement.
IsoXTargetz said:
Yeah, it doesn't really add up and so I don't really know what do with it.

#3:
Tiffany has 34 animals. She has 3 times as many birds as cats. She has 4 times as many cats as dogs. How many of each does she have?
For this one I got:
34 = B+C+D
Birds = 3C
Cats = 4D
Be consistent with your variable names. In the first equation you have B, C, and D, which are fine, as it's clear they represent the number of birds, cats, and dogs, respectively. In your 2nd and 3rd equations, you switch to Birds and Cats instead of B and C.

For this problem you're on the right track (barring the inconsistent variable names). You must have some examples of techniques for solving a system of equations -- use them.
IsoXTargetz said:
Then I got put into a loop of plugging in values, so I need help building the equations with this one too.

As already mentioned, give a name to each variable, possibly like this:
Let L = the largest no.
Let S = the smallest no.
Let O = the other no. (the middle number).

Instead of "_ + _ +_ = 32" and "Sum of the two smaller #S = L-8", write equations using the variable names.
Which one is Dat? Which one is David? Define variable names so that their meanings are clear.

Huh? Who is he and who is him? This is about as unclear as it could possibly be. Surely this is not the original problem statement.
Be consistent with your variable names. In the first equation you have B, C, and D, which are fine, as it's clear they represent the number of birds, cats, and dogs, respectively. In your 2nd and 3rd equations, you switch to Birds and Cats instead of B and C.

For this problem you're on the right track (barring the inconsistent variable names). You must have some examples of techniques for solving a system of equations -- use them.
I got both problems down now #1 and #3, I just don't get #2. Yes it is correctly written out and I got confused just as you. But I assume that he is referring to Dat and him is referring to David.

Can someone help me get an equation out of #2, I can't seem to reach a conclusion. It just loops, and I'm not sure how to model 38 years into the equation. Anyone?

Mark44
Mentor
IsoXTargetz said:
#2: Dat is 10 years older than David. 38 years ago, he was twice as old as him. How old is David now?
This was one of my equations that I tried to come up with:
Y = D+10
Y = 2D + 38
Here's a restatement of the problem to make it clearer.
Dat is 10 years older than David. 38 years ago, Dat was twice as old as David. How old is David now?

First, define a couple of variables.
Let D = David's age, now.
Let Y = Dat's age, now.

Your first equation is a correct interpretation of the first sentence. Your second equation is not correct. Based on the two definitions just above, what expressions represent David's and Dat's ages 38 years ago?