Question

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

Answer 1

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`