Subjects algebra

Percentage Changes

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1. Problem 1: Number of tourists difference between 1993 and 2000. The number of tourists decreases by 10% per year starting from 1990 with 12000 tourists. Formula: $N_t = N_0 \times (1 - r)^t$ where $N_0$ is initial number, $r$ is rate of decrease, $t$ is years after 1990. Calculate tourists in 1993: $t=3$, $$N_{1993} = 12000 \times (1 - 0.10)^3 = 12000 \times 0.9^3 = 12000 \times 0.729 = 8748$$ Calculate tourists in 2000: $t=10$, $$N_{2000} = 12000 \times 0.9^{10} = 12000 \times 0.3486784401 \approx 4184$$ Difference: $$8748 - 4184 = 4564$$ 2. Problem 2: Ziad's bank account in 2000. Ahmed's 2000 amount: 120000 EGP. Ahmed's 2010 amount after 20% increase: $$120000 \times 1.20 = 144000$$ Ziad's 2010 amount equals Ahmed's 2010 amount: 144000. Ziad's amount decreased by 10% from 2000 to 2010, so: $$Z_{2010} = Z_{2000} \times 0.90 = 144000$$ Solve for $Z_{2000}$: $$Z_{2000} = \frac{144000}{0.90} = 160000$$ Answer: 160000 EGP (option B). 3. Problem 3: Tony's salary after two years. Initial salary: 4600. After 10% increase first year: $$4600 \times 1.10 = 5060$$ After 3% decrease second year: $$5060 \times 0.97 = 4908.2$$ Answer: 4908.2 (option C). 4. Problem 4: Price of cheese in 2012. Original price 2010: 20. Increase 7% in 2011: $$20 \times 1.07 = 21.4$$ Decrease 8% in 2012: $$21.4 \times 0.92 = 19.688$$ Answer: 19.688 (option B). 5. Problem 5: Price Amira paid for the car. Lucas bought for 3500. Lucas lost 12% selling to Brad: $$3500 \times 0.88 = 3080$$ Brad gained 5% selling to Amira: $$3080 \times 1.05 = 3234$$ Answer: 3234. 6. Problem 6: Myriam's bank account growth. Initial deposit: 10000. First 3 years at 5% compounded annually: $$10000 \times 1.05^3 = 10000 \times 1.157625 = 11576.25$$ Next years at 8% compounded annually (number of years not specified, so formula given): $$A = 11576.25 \times (1.08)^n$$ where $n$ is number of years after first 3 years. Final answers: 1) 4564 tourists more in 1993 than 2000. 2) Ziad's 2000 bank account: 160000 EGP. 3) Tony's salary after 2 years: 4908.2. 4) Cheese price in 2012: 19.688. 5) Amira paid: 3234. 6) Myriam's account after 3 years: 11576.25, then grows at 8% compounded annually.