I need help with this math problem?

Question

3 ducks and 2 ducklings weigh 32kg. 4 ducks and 3 ducklings weigh 44 kg. All ducks weigh the same and all ducklings weigh the same . What is the weight of two ducks and one duckling?

also could you guys show your work and explain it to me so i understand it?

Thanks doug, but why do u multiply the first equation by 3 and the second equation by 2?

Answer 1

ok...this is called simultaneous equations (or somethin like that...doesnt really matter). You have to set up 2 equations. Each 1 will have two variables, lets just use "X" for ducks, and "d" for ducklings. u use the information given in the question to set up the two equations. First, it says that 3 ducks and 2 ducklings weigh 32 kg. So, this gives us the equation of:
3x+2d=32
and then, u use the second example to give the second equation. It says that 4 ducks and 3 ducklings weigh 44 kg. So, this gives us the equation of:
4x+3d=44
To say again, we have now:
3x+2d=32
4x+3d=44
Those are our two equations.
Now, the way this works is that u have to get rid of one of the variables, in both equations, so that in each equation u have only one variable (and it has to be the same one, either x or d). It does not matter which one u eliminate but I will eliminate "x". U eliminate "x" by making there the same number of "x"s on each equation, but one negative and one positive. I will show u how this is done.
-4(3x+2d=32)
3(4x+3d=44)
The least common multiple of 3 and 4 is 12 right? So, u want to get in one equation, 12x, and in the other -12x. This is because 12x and -12x cancel each other out. Now u do that by multiplying 3 by -4, and 4 by 3. This will give u 12 and -12. (u could have also done 3 times 4 and 4 times -3, it doesnt make a difference. Because mathematics says that u have to do an operation to both sides of an equation, whenn u multiply the "x"s by something, you must multiply the whole equation by that. So,
-4(3x+2d=32)= -12x-8d=-128.
3(4x+3d=44)= 12x+9d=132.
The 12x and the -12x canccel, so now u have;
-8d=-128
9d=132
now, u have to add the two equations together, so as to be able to solve for "d". when u add them u get:
-8d+9d=-128+132, and simplify to get
d=4.
so now u know that each duckling weighs 4 kg. U use this correct equation, and stick it in place of d for one of the equations. So let's use the first equation:
3x+2d=32 now becomes
3x+8=32 (because 4 times 2 =8.)
with that u can find:
3x=32-8, and then
3x=24
x=24/3, and so
x=8. So now u know that each duck weighs 8 kg, and each duckling weighs 4 kilograms. U can check that this is correct by trying it out on the second equation.
4x+3d=44,
and yes,
32+12=44, and so u know that ure answer is correct.

Did I explain all of this correctly, because it is hard to understand. I also have 1 other question, what grade are u guys taking this in?
Hope that helps :)

Answer 2

let ducks be equal to x and ducklings y.

Set it into the two equations

3x+2y=32
4x+3y=44

If you are familiar with solving linear systems, you know that least common multiple (lcm). So, let's try cancelling out y. the LCM OF 2 AND 3 IS 6. Therefore,

3[3x+2y=32]
2[4x+3y=44]

Simplifying then subtracting,

9x+6y=96
( - )8x+6y=88
_________
x+0y=8
x=8
Substituting back into the first equation,

3x+2y=32
3(8)+2y=32
2y=8
y=4

Going back to the representation of let ducks be equal to x and ducklings y, we now know that there are 8 ducks and 4 ducklings. Using this data, we can now proceed on solving for the question, the weight of two ducks and a duckling.

Make another equation

2x+y=?

Substitute the values of x and y

2(8)+4=?
?=20.

Therefore, the weight of two ducks and one duckling is 20kg

Answer 3

x = # od ducks
y = # of ducklings Then
3x+2y = 32 and
4x +3y = 44 Multiply the 1'st equation by 3 and the 2'nd equation by 2 to get
9x + 6y = 96 and
8x + 6y = 88 Now subtract the bottom equation from the top to get
x = 8 and substitute 8 for x in any of the equations to get y = 4. Then
2x + y = 2*(8) + 4 = 20

The moral of this story is: When doing math, you need to keep your ducks lined up in a row.

HTH ☺

Doug

Answer 4

let x = number of kg in duck's weight
y= " " duckling "

3x + 2y = 32 (i)
4x + 3y = 44 (ii)

multiply (i) by 3 and (ii) by 2 to get equal coefficients for "y"

9x + 6y = 96 .... which is (i*3)
8x + 6y = 88 .... which is (ii*2)

subtract to get
x = 8 ... substitute this back into (i)
3x + 2y = 32 (i)
3*8 + 2y = 32 (i)
24 + 2y = 32 (i)
2y = 8
y = 4

this tells us that
x = ducks = 8
y = ducklings = 4

the question:
"What is the weight of two ducks and one duckling?"

becomes:
2*8 + 1*4 = 16 + 4 = 20

20 kg is that weight.

Hopefully the steps I included will make the path to the solution of this problem clear enough.

My suggestion: if you're taking an algebra class, do ALL of the assigned homework and hten go back and do ALL of the rest of the problems in your text. When solutions bebcome simple, you will then understand the wisdom of doing this extra work. It really does help (I've been there)

good luck

Answer 5

2 ducks and one duckling would weigh 20 kg. How?
sol.
let x be the weight of one duck and y be the weight of one duckling,
3 ducks and 2 ducklings weigh 32kg will be 3x+2y=32kg(eq. 1), while 4 ducks and 3 ducklings weigh 44 kg will be 4x+3y=44kg(eq. 2).

multiply 3x+2y=32kg by 3 and multiply 4x+3y=44kg by -2 which will result to:
9x+6y=96kg(3) and -8x-6y=-88kg(4)

next, add (3) and (4). It will result to x=8kg. so the weight of one duck is 8kg.
substitute 8kg in any of the equation.
3x+2y=32kg ---> 3(8kg) + 2y=32kg
24kg + 2y = 32kg
24kg-24kg + 2y = 32kg - 24kg (whatever you subtract or add or multiply or divide in a side of the = sign, you should do it in the other side of the + sign so that the equation will still be balance or equal.)
2y/2 = 8kg/2
y = 4kg -----> this is the weight of one duckling.


IF A DUCK WEIGHS 8KG AND A DUCKLING WEIGHS 4KG, THEN 2 DUCK AND ONE DUCKLING WILL WEIGH 20kg

Answer 6

21

Answer 7

Let denote ducks by D
and duckings by Dg
From the first statement we get
3D+2Dg=32 --------------------1
and from sec statement
4D+3g=44 --------------------2
The ques is 2D+1Dg=?
Multiply eq 1 by 4 we get
12D+8Dg=128
and multiply eqn 2 by 3
12D+9Dg=132
substract last two eqns
Dg=4
And D =6

plug these values in ques eqn
2D+1Dg=?
16+4=20---Answer