Math - Trigonometry

Question

The Covid-19 cases in Magnayon City are rapidly increasing day after day and you want to extend help and distribute the 72 boxes of relief goods in the four quarantine facilities in your area based on the number of families residing in the said facility. Assuming that the number of boxes is enough for the four facilities, with 2√x number of families in Facility A, √25x number of families in Facility B, 2√16x number of families in Facility C and √x in Facility D.

1.Solve for x.

2.How many boxes of relief goods will be distributed to each facility?

3.Which facility will receive the highest number of boxes of relief goods?

4.Which facility will receive the lowest number of boxes of relief goods?

B. The government issued a financial support with a total of P64,000 for the four facilities depending on the number of families residing in the said facility.

1.How much will each quarantine facility receive?

2.Facility C decided to distribute the money to the people in their facility, regardless of age. If there are 85 people in Facility C, how much will each of them receive?

Facility B decided to distribute the money to each family in their facility, regardless of how many people are there. If there are 15 families in Facility B, how much will each family receive?

Answer 1

72 = 2√x + 5√x + 4√x + √x

72 = 12√x

Solve for x and answer the questions that follow.

Answer 2

Question A)

Facility A has 2√x families,

Facility B has √25x families = 5√x families,

Facility C has 2√16x families =8√x families

Facility D has √x families

A-1)A + B + C + D = 72 => 2√x+5√x +8√x+√x = 16√x = 72

=> √x = 4.5 => x = 20.25

A-2) then A gets 2(4.5) = 9, B gets 5(4.5) = 22.5. C gets 8(4.5) = 36, D gets 4.5

A-3) The highest is C

A-4) The lowest is D

Question B)

B-1)The easy way to calculate the amount of money each facility gets is to multiply the number of boxes each facility gest by ($64,000/72)

then A gets 9($64000/72) =$8,000, B gets 22.5($64000/72) =$20,000. C gets 36($64000/72) =$32,000, and

D gets 4.5($64000/72) =$4,000

B-2) $32,000/85 = $376.5

B-3)$20,000/15 = $1,333.3