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Question

How much does each pumpkin weigh?
3 different sized pumpkins put together weigh 43 kg. middle sized pumpkin weighs 3 times more than the smallest pumpkin. the largest pumpkin weighs 3kg more than the other 2 together

How much does each pumpkin weigh?

Answer 1

lets a be the weight of the smallest
the middle weigths 3a
the largest weights a+3a +3

so the three weight a+3a +a+3a +3 = 43

or 8a+ 3 = 43 solving a= 5kg


the middle weights 15 kg

and the big a+3a+5 = 23 kg

Answer 2

Big = B
Middle = M
Small = S

B + M + S = 43 Given

M = 3S Given

B = M + S + 3 Given

From total weight formula let us proceed...

B + M + S = 43
We said M = 3S
So substitute 3S for M

B + 3S + S = 43 or B + 4S = 43 FORMULA ONE

Now We also said...
B = M + S + 3
and M = 3S
So if you substitute 3S for M, you get...

B = 3S + S + 3 or B = 4S + 3 FORMULA TWO

Now, since you have an equivalent for "B",
use it in FORMULA ONE

FORMULA ONE B + 4S = 43
FORMULA TWO B = 4S + 3
Substitute the "4S + 3" value of B into Formula One...

4S + 3 + 4S = 43 and solve for "S"
8S + 3 = 43
8S = 40
S = 5

We now know that the Small pumpkin weighs 5 Kg.

At the top we said that the middle size was 3 times the small one.
or M = 3S
So, the Middle size pumpkin is 3 x 5 Kg = 15 Kg

And the sum of all the pumpkins was 43 Kg,
So B + 15 Kg + 5 Kg = 43 Kg
B + 20 Kg = 43 Kg
B = 23 Kg Check: 23 + 15 + 5 = 43 Correct

So the Big Pumpkin weighs 23 Kg

Regards,
Zah

Answer 3

x+y+z = 43 ...(i)
y = 3x ...(ii)
z = x+y+2 ...(iii)

substitute y in (iii)
z = 3x + x + 3 = 4x + 3

from (i)
x + 3x+ 4x+3 = 43
or, 8x= 40
or, x=5

y=15
z=23