Question

A farmer grows x acres of peas and y acres of tomatoes. He has 12 acres available to plant peas and tomatoes. Write an inequality in x and y to satisfy this condition. The number acres of tomatoes planted must not be more then twice the number of acres of peas planted. Write an inequality in x and y to satisfy this condition.​

Answer 1

The conditions set by the farmer can be represented by two inequalities: x + y ≤ 12, stating that the total area for planting must not exceed 12 acres, and y ≤ 2x, which indicates that the area for tomatoes must not be more than twice the area for peas.

Step-by-step explanation:

The question involves forming inequalities to describe two different conditions involving areas for planting peas and tomatoes. The first condition states that a farmer has a total of 12 acres to plant both peas and tomatoes. The inequality representing this condition would be:

x + y ≤ 12

where x is the number of acres of peas and y is the number of acres of tomatoes. This equation states that the sum of the acres used for planting peas and tomatoes must not exceed 12 acres.

The second condition states that the number of acres of tomatoes planted must not be more than twice the number of acres of peas planted. The inequality representing this is:

y ≤ 2x

This means that for every acre of peas planted, up to two acres of tomatoes can be planted. Both inequalities must be true to satisfy the conditions set by the farmer.

Answer 2

Y < 2X

Step-by-step explanation:

Let the acres of land on which pea is to be cultivated is "X" acres and the acres of land on which tomato is to be cultivated is "Y"

It is given that number acres of tomatoes planted must not be more then twice the number of acres of peas planted

Thus,
`Y < 2X`

`X + Y = 12` acres

`Y = 12-X` acres

Thus,

`12 - X \leq X\\12\leq 2X\\6 \leq X`

Let us take X = 6 , Then Y = 13-6 = 6