Question

four pumpkins weigh 26 pounds altogether. Pumkin one weighs four less than three times the weight of Pumkin threee. Pumkin four weighs twice as much as pumkin One. Pumpkin Two weighs five more pounds than Pumkin three. What does each pumpkin weigh

Answer 1

5, 8, 3, 10 lbs.

Explanation:

We can solve this using a system of equations! We will call pumpkins
`a, b, c, d`.

Our equations are thus:

`a + b + c + d = 26`

`a = 3c - 4`

`d = 2a`

`b = c + 5`

So now we just need to solve this system of equations.

We can start by solving for the value of pumpkin
`c` and go from there. So first we substitute some equations around.

First we write out pumpkin
`d` in terms of
`a`.

`d = 2a = 2(3c - 4) = 6c - 8`

And now we put the three equations into the first equation:

`a + b + c + d = 26\\(3c-4)+(c+5)+(c)+(6c-8)=26`

Then we simplify to get:

`11 c - 7 = 26`

`11c = 33\\c = 3`

So we know pumpkin
`c` weighs 3 pounds.

Then we use the equations from before to get the value of the other pumpkins:

`a = 3c-4 = (3*3)-4=9-4=5\\d = 2a = 2*5=10\\b = c + 5 = 3 + 5 = 8`

And we can check our results by putting into first equation:

`5+8+3+10=26`

So it works out!

Thus our pumpkins weigh 5, 8, 3, 10 lbs each.