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- Word problem: Marites is a fish vendor that opened up her own fish store. Marites stated that the profit P she earns for selling x number of fish products can be modelled as p(x) = x2 - 35x + 1200. She wondered how many fish she could sell to earn at most 950 pesos worth of profit?
- Given: x2 – 35x + 1200 ≤ 950 x2 – 35x + 1200 – 950 < 0x2 – 35x + 250 = 0(x – 25) (x – 10) = 0x - 25 = 0 x - 10 = 0x = 25 x = 10
- SOLUTIONS
- SOLUTIONS
- Testing points: x2 – 35x + 1200 ≤ 950x < 10 = 010 < x < 25 = 11x > 25 = 26
- SOLUTIONS
- x2 – 35x + 1200 ≤ 950; 11(11)2 – 35(11) + 1200 ≤ 950121 – 385 + 1200 ≤ 950936 ≤ 950 TRUE
- x2 – 35x + 1200 ≤ 950; 0(0)2 – 35(0) + 1200 ≤ 9500 - 0 + 1200 ≤ 9501200 ≤ 950 FALSE
- SOLUTIONS
- x2 – 35x + 1200 ≤ 950; 26(26)2 – 35(26) + 1200 ≤ 950 676 – 910 + 1200 ≤ 950 -234 + 1200 ≤ 950 966 ≤ 950 FALSE
- Answer: The solution to the inequality x2 - 35x + 1200 ≤ 950 is [x | 10 ≤ x ≤ 25]. The number of fish products that must be bought with at most 950 pesos is greater than or equal to 10 but less or equal to 25.
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