Chapter 8, Problem 4PT

To determine

To find: The ways can Conrado arrange the pumpkin so that he has at least rows of pumpkins.

Answer to Problem 4PT

The Conrado can arrange the pumpkinin following ways.

  $4$ Rows, $35$ pumpkins

  $5$ Rows, $28$ pumpkins

  $7$ Rows, $20$ pumpkins

  $10$ Rows, $14$ pumpkins

  $14$ Rows, $10$ pumpkins

  $20$ Rows, $7$ pumpkins

Explanation of Solution

Given information:

The given information is:

Total Pumpkins = 140,

At least $4$ rows of pumpkins and at least $6$ rows of pumpkins

Calculation:

Atleast $4$ rows of pumpkins:

  $\left(x+4\right)$

Atleast $6$ rows of pumpkins:

  $\left(y+6\right)$

The equation for this problem is $\left(4+x\right)\left(6+y\right)=140$ . You find the number of pumpkins by multiplying number or rows by number of columns.

  $\left(4+x\right)\left(6+y\right)=140$

Now, you can plug in numbers for $x$ since the number of pumpkins in each row depends on how many rows there are. When there are $4$ rows $\left(x=0\right)$ , there are $35$ pumpkins in each row $\left(y=29\right)$ . You can either do it by hand and plug in whole numbers in for $x$ that can produce positive (because at least $4$ rows are needed) whole numbers(you cannot have part of a pumpkin) for $y$ or plug it in graph. Keep plugging in values for $x$ that give a positive whole value of $y$ until $y$ becomes negative.

  $4$ Rows, $35$ pumpkins

  $5$ Rows, $28$ pumpkins

  $7$ Rows, $20$ pumpkins

  $10$ Rows, $14$ pumpkins

  $14$ Rows, $10$ pumpkins

  $20$ Rows, $7$ pumpkins

Therefore, the Conrado canarrange the pumpkinin following ways.