有條關於 Partial Variation 既題目想問下大家 ~ (主要想問紅字部分)

The school soccer team organizes a soccer training camp. The school subsidizes two-thirds of the total expenses and the team members share the remaining expenses. The total expense $E for the camp is partly constant and partly varies directly as the number of team members N joining the camp.

If 15 members join the camp, the school has to pay $2400;
if 20 members join the camp, the school has to pay $3000.

(a) What is the total expense if 20 members join the camp?
(b) Express E in terms of N.
(c) If 30 members join the camp, how much should each member pay?
(d) If each member pays $72, how many members joined the camp?

先謝

a) 3000/(2/3)=$4500 (因為The school subsidizes two-thirds of the total expenses)

b) E=aN+b, where a, b are constants...然後用two equation in two unknown計(因為計埋比你有多d明彩啦)

4500=a(20)+b ------------------------------------------------------------------------(1)
3600=a(15)+b-------------------------------------------------------------------------(2)

(如果有program, 呢到可以篤機, 但係我del左 )

(1)-(2) 5a=900
----------a=180

3600=180(15)+b===>b=900

E=180N+900

c) sub數, (180(30)+900)*(1/3)*(1/30)=$70

d) 太複雜無心機計

利申: 數學DSE 做唔切

(a)
If 20 members join the camp,
E * (2/3) = 3000
E = 4500
∴ Total expenses = $4500

(b)
If 15 members join the camp,
E * (2/3) = 2400
E = 3600

E = k₁ + k₂N　where k₁ and k₂ are non-zero constants.

When E=4500 and N=20,　（ from (a) ）
4500 = k₁ + 20 k₂　--------- (1)

When E=3600 and N=15,
3600 = k₁ + 15 k₂　--------- (2)

我Skip steps ...

Solving (1) and (2),
k₁ = 900
k₂ = 180
∴ E = 900 + 180N

(c)
When N = 30,
E = 900 + 180 * 30
E = 6300

Each member should pay
$6300 * (1/3) / 30
=$70

(d)
E * (1/3) = 72N
E = 72N * 3
900 + 180N = 72N * 3
36N = 900
N = 25
∴ 25 members joined the camp.