# Systems of Equations word problems

• IsoXTargetz
In summary, 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?
IsoXTargetz
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.

IsoXTargetz said:
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.

IsoXTargetz said:
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.

Mark44 said:
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?

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?

## What are "Systems of Equations word problems"?

Systems of Equations word problems are mathematical problems that involve multiple equations and multiple unknown variables. The goal is to find the values of the unknown variables that satisfy all of the equations.

## Why are Systems of Equations word problems important?

Systems of Equations word problems are important because they allow us to model real-life situations and make predictions or solve problems using mathematical equations. They are also a fundamental concept in algebra and are often used in higher level math courses and in science and engineering fields.

## How do you solve Systems of Equations word problems?

To solve Systems of Equations word problems, you must first identify the unknown variables and set up equations using the given information. Then, you can use algebraic techniques such as substitution or elimination to solve for the values of the unknown variables. Finally, you must check your answers to make sure they satisfy all of the equations.

## What are some common types of Systems of Equations word problems?

Some common types of Systems of Equations word problems include mixtures, work, distance-rate-time, and money problems. These types of problems often involve multiple quantities that are related to each other and can be modeled using equations.

## How can I improve my problem-solving skills for Systems of Equations word problems?

To improve your problem-solving skills for Systems of Equations word problems, it is important to practice and familiarize yourself with different types of problems. You can also break down the problem into smaller parts and use diagrams or tables to organize the information. It is also helpful to double check your work and make sure your answers make sense in the context of the problem.

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