Systems of Equations word problems

[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.

Please help me!

 

[Deleted member 4993]

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.

Let the numbers be:

L = largest

S = smallest

M = middle number

We know:

L = 4 * S ...............(1)

L + M + S = 32 .......(2) → ..................................M + 5*S = 32 .........(4)

M + S = L - 8 .........(3) → M + S = 4 * S - 8 → ....M - 3*S = -8 .........(5)

Now use (4) and (5) to solve for M and S. Then use (1) to solve for L


#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.

Please help me!

.

 

[Steven G]

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 This may or may not be correct. You MUST define YOUR variable. I'll assume that D is David's age NOW and D + 10 is Dat's age now.
What is David's age 38 years ago? What is Dat's age 38 years ago? What do you know about these ages?
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 correct
Birds = 3C correct
Cats = 4D You have some number of dogs. Cats = 4D says the number of Cats is 4 times the number of dogs. Is this true? You also should have written that C=4D
Then I got put into a loop of plugging in values, so I need help building the equations with this one too.

Please help me!

I'll assume that B=# of birds, c=# of cats and D = # of dogs

 

[IsoXTargetz]

Okay!
So I have finished both of those equations, and I finally reached an answer to the cats, birds, dogs word problem!
Except #2. Can someone please help me on starting out with number 2. No matter how much I think about it, I can't seem to get an equation out of it! Please help me!

 

[Deleted member 4993]

Dat is 10 years older than David. 38 years ago, he was twice as old as him. How old is David now?

What are you supposed to find? → David's age now

Let

David's age now = D

"Dat is 10 years older than David" → Dat's age now = D + 10

38 years ago:

David's age = D - 38

Dat's age = D - 28

38 years ago, he (Dat) was twice as old as him(David) → D - 28 = 2*(D - 38)

Now continue....

 

[Ishuda]

Okay!
So I have finished both of those equations, and I finally reached an answer to the cats, birds, dogs word problem!
Except #2. Can someone please help me on starting out with number 2. No matter how much I think about it, I can't seem to get an equation out of it! Please help me!

Since question is How old is David now, D_t (your Y) is age Dat now; D_d (your D) is the age of David now.

The first equation is correct: Dat is 10 years older than David. Well obviously D_t > D_d so
D_t = D_d + 10

The second equation is wrong: 38 years ago, he (Dat) was twice as old as him (David). Well 38 years ago Dat was D_t-38 and David was D_d-38. So 38 years ago
D_t-38 = 2 (D_d-38)
You have the D_t-38 but you forgot to put the minus 38 with D_d