ducky promenade

Question

three big ducks went out one day

with two ducklings behind.

fourteen kilograms was their weight

when all 5 were cokmbined.

 

add one duck and one duckling

and their weight increased.

nineteen kilograms was the total

of the seven with webbed feet.

 

if all ducklings have one weight

and ducks all have another.

then you should find the total weight

of three, one child two mothers.

 

Answer 1

Let B = big duck

Let S = small duck or duckling

 

equation 1)  3B + 2S = 14   3 big ducks and 2 ducklings totaled 14 kg

equation 2)  4B + 3S = 19   4 big ducks and 3 ducklings totaled 19 kg

 

We have two equations with 2 unknowns.

Use elimination to solve the system.

Multiply equation 1 by 3 and equation 2 by -2 and add..

 

 9B + 6S = 42

-8B - 6S  = -38

-------------------

B = 4 kg

 

Plug that back into equation 1 to find S

 

3(4) + 2S = 14

12 + 2S = 14

2S = 2

S = 1 kg

 

Mother ducks weigh 4 kg, ducklings weigh 1 kg

 

2 mothers and 1 child weigh

2(4) + 1 = 9 kg

 

Answer 2

Let x = weight of big ducks

     y = weight of duckling

 

Translate:

"three big ducks went out one day
with two ducklings behind.
fourteen kilograms was their weight
when all 5 were combined."

    means    3x + 2y = 14      [eq1]

 

"add one duck and one duckling
and their weight increased.
nineteen kilograms was the total
of the seven with webbed feet."

    means    4x + 3y = 19      [eq2]

 

"if all ducklings have one weight
and ducks all have another.
then you should find the total weight
of three, one child two mothers."

    means    find 2x+y

 

 3x + 2y = 14      [eq1]

 4x + 3y = 19      [eq2]

 

  9x +  6y =  42     [3*eq1]

  8x +  6y =  38     [2*eq2]

-------------------     [elimination; subtract equations]

    x           = 4        [eq3]

            x   = 4 kg

 

 3x + 2y = 14      [eq1 again]

 3x         = 12       [3*eq3]

-------------------     [elimination; subtract equations]

         2y =  2

           y = 1 kg

 

      2x + y = 9 kg

 

Checking (very important):

  Is  3(4) + 2(1) = 14   ?

        12  +  2  = 14   ?

          14 = 14   ? yes

  is  4(4) + 3(1) = 19   ?

       16  + 3  = 19   ?

           19 = 19   ? yes

 

Answer 3

 Let x = big duck
Let y = duckling

3x + 2y = 14  ____________equation 1
4x+ 3y = 19 _____________equation 2


Multiply equation 1 by 3 and equation 2 by -2 and add..

9x + 6y = 42
-8x - 6y = -38
-------------------
x = 4 kg

Plug that back into equation 1 to find y

3(4) + 2y = 14
12 + 2y = 14
2y = 2
y = 1 kg

Mother ducks weigh 4 kg, ducklings weigh 1 kg

 

Total weight 

2 mother=2(4)=8

1 child=1

 

8+1=9kg

2 mothers and 1 child weigh
2(4) + 1 = 9 kg