In a sale promotional campaign by Assamadiya frozen foods on 02/01/2025,80% of first new year Monday (02/1/2015),slaughtered cows is given out to customer as free beef prizes based on on previous years patronage. There are free beef prizes altogether, the first prize winner gets 10,950 kgs of beef,the second gets 3,645 kgs the third 1,215 kgs as so on. how much beef(kgs) does the eight person get? how much free prizes is there altogether how much beef (kgs) was realized on first new year Monday (]2/01/2025) Assuming each kilogram of beef cost 800 naira,what is the total value of beef realized from the slaughtered cows on the new year? if the inflationary trend increasing by 2% monthly,what would have been the total value of beef realized from the slaughtered cows as at 01/12/2025?

Question

Asked on June 11, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-06-11T19:31:38.561Z

Step 1: Calculate the amount of beef the eighth person gets. The prizes form a geometric progression. The first term is a_1 = 10,950 kgs. The common ratio r is found by dividing the second term by the first term: r = (3,645)/(10,950) = (1)/(3) The formula for the n-th term of a geometric progression is a_n = a_1 · r^n-1. For the eighth person (n=8): a_8 = 10,950 · ((1)/(3))^8-1 a_8 = 10,950 · ((1)/(3))^7 a_8 = 10,950 · (1)/(2187) a_8 = (10,950)/(2187) a_8 = 5 kgs The eighth person gets 5 kgs of beef. Step 2: Determine the total number of free prizes. We need to find the number of terms n for which the prize amount a_n is at least 1 kg (a reasonable minimum for a "prize"). a_n = 10,950 · ((1)/(3))^n-1 1 ((1)/(3))^n-1 (1)/(10,950) 3^n-1 10,950 To solve for n-1, we take the logarithm base 3 of both sides: n-1 _3(10,950) Using the change of base formula, _3(10,950) = ((10,950))/((3)): n-1 (9.301)/(1.0986) ≈ 8.466 n 9.466 Since n must be an integer, the maximum number of prizes is 9. There are 9 free prizes altogether. Step 3: Calculate the total beef (kgs) realized on 02/01/2025. First, calculate the total amount of beef given as prizes (S_9), which is the sum of the first 9 terms of the geometric progression. The formula for the sum of a geometric series is S_n = (a_1(1-r^n))/(1-r). S_9 = (10,950 (1 - (1)/(3))^9)1 - (1)/(3) S_9 = (10,950 (1 - 1)/(19683))(2)/(3) S_9 = (10,950 (19682)/(19683))(2)/(3) S_9 = 10,950 · (19682)/(19683) · (3)/(2) S_9 = 10,950 · (9841)/(6561) S_9 = 16,425 kgs This amount (16,425 kgs) represents 80% of the total beef realized from slaughtered cows. Let X be the total beef realized. 0.80 · X = 16,425 kgs X = (16,425)/(0.80) X = 20,531.25 kgs The total beef realized on 02/01/2025 was 20,531.25 kgs. Step 4: Calculate the total value of beef realized from the slaughtered cows on the new year. The total beef realized is 20,531.25 kgs (from Step 3). The cost per kilogram is 800 naira. Total value = Total beef × Cost per kg Total Value = 20,531.25 kgs × 800 naira/kg Total Value = 16,425,000 naira The total value of beef realized was 16,425,000 naira. Step 5: Calculate the total value of beef realized as at 01/12/2025, assuming a 2% monthly inflation. The initial value (PV) on 02/01/2025 is 16,425,000 naira (from Step 4). The monthly inflation rate is r = 2\% = 0.02. The number of months (n) from 02/01/2025 to 01/12/2025 is 11 months (February, March, April, May, June, July, August, September, October, November, December). The future value (FV) with compound inflation is given by FV = PV · (1 + r)^n. FV = 16,425,000 · (1 + 0.02)^11 FV = 16,425,000 · (1.02)^11 FV = 16,425,000 · 1.24337385... FV ≈ 20,429,999.25 naira The total value of beef realized as at 01/12/2025 would have been 20,429,999.25 naira. Send me the next one 📸

Accepted Answer · 2026-06-11T19:31:38.561Z

Step 1: Calculate the amount of beef the eighth person gets. The prizes form a geometric progression. The first term is a_1 = 10,950 kgs. The common ratio r is found by dividing the second term by the first term: r = (3,645)/(10,950) = (1)/(3) The formula for the n-th term of a geometric progression is a_n = a_1 · r^n-1. For the eighth person (n=8): a_8 = 10,950 · ((1)/(3))^8-1 a_8 = 10,950 · ((1)/(3))^7 a_8 = 10,950 · (1)/(2187) a_8 = (10,950)/(2187) a_8 = 5 kgs The eighth person gets 5 kgs of beef. Step 2: Determine the total number of free prizes. We need to find the number of terms n for which the prize amount a_n is at least 1 kg (a reasonable minimum for a "prize"). a_n = 10,950 · ((1)/(3))^n-1 1 ((1)/(3))^n-1 (1)/(10,950) 3^n-1 10,950 To solve for n-1, we take the logarithm base 3 of both sides: n-1 _3(10,950) Using the change of base formula, _3(10,950) = ((10,950))/((3)): n-1 (9.301)/(1.0986) ≈ 8.466 n 9.466 Since n must be an integer, the maximum number of prizes is 9. There are 9 free prizes altogether. Step 3: Calculate the total beef (kgs) realized on 02/01/2025. First, calculate the total amount of beef given as prizes (S_9), which is the sum of the first 9 terms of the geometric progression. The formula for the sum of a geometric series is S_n = (a_1(1-r^n))/(1-r). S_9 = (10,950 (1 - (1)/(3))^9)1 - (1)/(3) S_9 = (10,950 (1 - 1)/(19683))(2)/(3) S_9 = (10,950 (19682)/(19683))(2)/(3) S_9 = 10,950 · (19682)/(19683) · (3)/(2) S_9 = 10,950 · (9841)/(6561) S_9 = 16,425 kgs This amount (16,425 kgs) represents 80% of the total beef realized from slaughtered cows. Let X be the total beef realized. 0.80 · X = 16,425 kgs X = (16,425)/(0.80) X = 20,531.25 kgs The total beef realized on 02/01/2025 was 20,531.25 kgs. Step 4: Calculate the total value of beef realized from the slaughtered cows on the new year. The total beef realized is 20,531.25 kgs (from Step 3). The cost per kilogram is 800 naira. Total value = Total beef × Cost per kg Total Value = 20,531.25 kgs × 800 naira/kg Total Value = 16,425,000 naira The total value of beef realized was 16,425,000 naira. Step 5: Calculate the total value of beef realized as at 01/12/2025, assuming a 2% monthly inflation. The initial value (PV) on 02/01/2025 is 16,425,000 naira (from Step 4). The monthly inflation rate is r = 2\% = 0.02. The number of months (n) from 02/01/2025 to 01/12/2025 is 11 months (February, March, April, May, June, July, August, September, October, November, December). The future value (FV) with compound inflation is given by FV = PV · (1 + r)^n. FV = 16,425,000 · (1 + 0.02)^11 FV = 16,425,000 · (1.02)^11 FV = 16,425,000 · 1.24337385... FV ≈ 20,429,999.25 naira The total value of beef realized as at 01/12/2025 would have been 20,429,999.25 naira. Send me the next one 📸

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