There are three pumpkins.Each two of them are weighed in pairs and the final results are: #12# #"kg"#, #13# #"kg"#, #15# #"kg"#, What is the weight of the lightest pumpkin?

Please help......Thanks

1 Answer
smendyka
Nov 2, 2016

The weight of the lightest pumpkin is #5kg#

Explanation:

If we weigh pumpkin 1 (let's call it #x#) and pumpkin 2 (let's call it #y#) we know these two added together are #12kg# so:

#x + y = 12kg#

Then solve for #y#
#y = 12kg - x#

Next, if we weigh pumpkin 1 (still calling it #x#) and pumpkin 3 (let's call it #z#) we know these two added together are #13kg# so:

#x + z = 13kg#

Then solve for #z#
#z = 13kg - x#

Next, if we weigh pumpkin 2 (still calling it #y#) and pumpkin 3 (still calling it #z#) we know these two added together are #15kg# so:

#y + z = 15kg#

But from above we know what #y# is in terms of #x# and we know what #z# is in terms of #x# so we can substitute this for #y# and #z# in this formula and solve for #x#:
# 12kg - x + 13kg - x = 15kg#
#25kg - 2x = 15kg#
#25kg - 15kg = 2x#
#2x = 10kg#
#x = 5kg#

Substituting the value of #x# back into the first formula and calculating #y# gives:
#y = 12kg - 5kg#
#y = 7kg#

And substituting the value of #x# back into the second formula and calculating #z# gives:
#z = 13kg - 5kg#
#z = 8kg#

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