1.
設加入 m 公克的食鹽。
混合食鹽水濃度
= [(m + 1360 x 10%) / (m + 1360)] x 100%
= (100m + 13600)% / (m + 1360)
(100m + 13600)% / (m + 1360) > 15% 及 (100m +13600)% / (m + 1360) < 20%
100m + 13600 > 15m + 20400 及 100m +13600 < 20m + 27200
85m > 6800 及 80m < 13600
m > 80 及 m < 170
所以 80 < m < 170
須加入食鹽多於 80 公克而少於 170 公克。
2.
設 f(x) = mx+ c ...... [1]
當x 的值減少 2,f(x) 的值增加 10 :
f(x) + 10 = m(x - 2) + c
f(x) = mx + c - (2m + 10) ...... [2]
[1] = [2] :
mx + c = mx + c - (2m + 10)
2m + 10 = 0
m = -5
所以 f(x) = -5x + c
f(-1) = 11
-5(-1) + c = 11
c = 6
所以 f(x) = -5x + 6
f(10)
= -5(10) + 6
= -44
3.
最臨界的情況,是票數平均分佈在五位候選人。每人得票
= 80000 ÷ 5 票
= 16000 票
只要多取一票,便可確定當選。
故此,確定當選的票數
= 16000 + 1 票
= 16001 票
4.
設每本書的成本為 c 元。
{[1 + (1/4)]c - 10} - c ≥ c x 5%
(1.25c - 10) - c ≥ 0.05c
0.20c ≥ 10
c ≥ 50
每本書的成本至少為 50 元。
參考資料 賣女孩的火柴
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