Question

3 Madam Esi used and of her x acres of land to cultivate mangoes and oranges respectively. (a) Express, in term of x, the number of acres of the land she used to cultivate: mangoes; oranges (b) If madam Esi used 20 more acres of land to cultivate oranges than mangoes, find the value of x. How many acres of land was used to cultivate mangoes? Calculate, correct to the nearest whole number, the percentage of the land that wa used.


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Answer 1

Madam Esi used 3/7 of her x acres for mangoes and 4/7 for oranges. She used 20 acres more for oranges than mangoes. The total land (x) is 140 acres, where 60 acres were used for mangoes, constituting approximately 43% of the total land.

Step-by-step explanation:

Madam Esi used 3/7 of her land to cultivate mangoes and 4/7 of her land to cultivate oranges. Given that she used x acres of land in total, we express the acres used for each fruit as follows:

• For mangoes: (3/7)x acres
• For oranges: (4/7)x acres

We are given that the acres used for oranges is 20 more than that used for mangoes. So, we set up the equation:

(4/7)x - (3/7)x = 20 acres

Simplifying, we get (1/7)x = 20 acres, and solving for x, we find that x = 140 acres.

Therefore, the amount of land used for mangoes would be:

(3/7) * 140 = 60 acres

To calculate the percentage of the land used to cultivate mangoes, we use the formula:

Percentage of land used for mangoes = (Acres used for mangoes / Total acres) * 100%

Substituting the values:

Percentage = (60/140) * 100% ≈ 42.86%, which rounds to 43%.