Chook Me!

How do you solve this?

Um so i've got 3 maths questions, which i dont know how to do. But please dont just post the answer without any explaination. The 1st one, Jim had 8 watches costing $800 each in his shop (which means all cost $6400), he sold 2 at a loss of 5% (?). What was the selling price for each of the two watches? If he sold the rest at 20% profit each, whats the total profit made from the sale of all the watches? Next, Hayden had $128 & Adrian had $36 (both had $164). After their dad gave each of them an equal amount, Hayden had twice as much as Adrian. How much did their dad give to each of them? I dont know if this is trail and error question but anyway. A duck cost $12 and a chicken at $9. On day 1, Sam sold 2/3 of his poultry and collected $4080. 3/5 of the poultry sold were chickens. How many ducks sold on day 1? And how many of the poultry were left after day 1? If you know how to do just one or two that will be appreciated too. Thanks =)

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1. PROBLEM 1: The two watches should have sold for $800 each. But he had to reduce them by 5% and sell them at a loss. (5% x $800 = 5/100 x 800 = $40). In other words he sold each at $760. 2 x $760 = $1520 The next 6 watches he sold at a 20% profit. 20% x $800 = 20/100 x 800 = $160). In other words he sold each for $960. 6 x $960 = $5760 In total he received $1520 + $5760 = $7280. The cost was 8 x $800 = $6400. Total profit amount was $7280 - $6400 = $880 or $110 per watch. To figure the profit, divide the additional amount made by the original cost: $110 / $800 = 0.1375 = 13.75% Answer: He made an overall profit of 13.75% PROBLEM 2: Let x be the amount given to them by their dad. Hayden now has 128 + x, Adrian now has 36 + x Hayden has twice as much as Adrian. 128 + x = 2(36 + x) Distribute the 2 through the parentheses: 128 + x = 72 + 2x Subtract x from both sides: 128 = 72 + x Subtract 72 from both sides: 56 = x Reverse: x = 56 Double-check: Hayden will have $184. Adrian will have $92. Hayden has double. Answer: $56 each PROBLEM 3: If 3/5 of the poultry were chickens, then 2/5 of the poultry were ducks. In other words, he sold 3 chickens for every 2 ducks sold. For each set of 5 birds (3 chickens and 2 ducks) he would make: 3 * $9 + 2 * $12 = $27 + $24 = $51 Dividing this into $4,080, you get: $4080 / $51 = 80 sets of 5 birds = 400 birds 3/5 were chickens (3/5 * 400 = 240 chickens) 2/5 were ducks (2/5 * 400 = 160 ducks) Let T be the total number of birds. 2/3 T = 400 T = 400 * 3/2 T = 1200/2 T = 600 Remember that 400 were sold, so subtract to get the number left. Answer: 160 ducks were sold (and 240 chickens) 200 birds were left after day 1
2. 2 watches cost $1600 Selling at a loss of 5% means he sold them for 5% less then he paid for them 5% of $1600 is 80 Therefore he sold the two watches for $1520 or $760 each Selling at 20% profit means he sold for 20% more than he paid 20% of $800 is $160 therefore he sold the remaining 6 watches for $960 each Total profit = total revenue = total cost total revenue = 2 watches sold at $760 each and 6 watches sold at $960 each = $7280 Total profit = $7280 - 6400 = $880 % profit = $880/$6400 = .1375 = 13.75%
3. H = $128 A = $36 X = Amount dad gives H+X = 2 (A+X) since after they received the money Adrian had half of Hayden H + X = 2A + 2X $128 + X = $72 + 2X $128 = $72 + X X = $56 Their dad gave them $56 dollars each.
4. 1) Number of watches = 8 Cost of each watch = $ 800 Total cost of the watches = 8 x 800 = $ 6,400 Jim sold 2 watches at a loss of 5%. Total cost of 2 watches = 2 x 800 = $ 1,600 a) If you lost 5%, it means that you sold it for 95% of price. ( 1 - 5% = 95%) what is 95% of 800 = .95 x 800 = $ 760.00 Each watch is sold at $ 760. For the 2 watches = 2 x 760 = $ 1,520 1,600 - 1,520 = $ 80 ==> loss for the 2 watches 80/ 1600 = .05 x 100 = 5% b) sell the remaining 6 watches at 20% profit each Price of each watch = 1.20 ( 800) = $ 960 Total profit for the 6 watches = 960 - 800 = 160 x 6 = $ 960.00 Net Profit for the 8 watches = 960 - 80 = $ 880 ====================== 2) $ 128 = Hayden had $ 36 = Adrian had Total money they had = 128 + 36 = $ 164 Let x = amount their dad gave them After giving x amount, Hayden's money is twice as much as Adrian's. (128 + x) = 2( 36 +x) 128 + x = 72 + 2x 128 - 72 + x - x = 72 - 72 + 2x - x 56 = x x = 56 Their dad gave them $ 56 each Hayden money = 128 + 56 = 184 Adrian money = 36 + 56 = 92 184 is twice of 92 ============================== 3) Cost of duck = $ 12 Cost of chicken = $ 9 Let D = number of ducks C = number of chickens P = total number of poultry D + C = P Total money on day 1 = $ 4,080 x = number of poultry sold on day 1 2/3 of the poultry was sold 1/3 of the poultry was left 3/5 of the 2/3 poultry sold were chickens = 3/5 x 2/3 = 6/15 2/5 of the 2/3 poultry sold were ducks = 2/5 x 2/3 = 4/15 (6/15)9x + (4/15) 12x= 4080 3.60x + 3.20x = 4080 6.80x = 4080 x = 600 ==> number of poultry sold 6/15 x 600 = 240 ===> number of chickens sold 4/15 x 600 = 160 ===> number of ducks sold How many poultry was left? 2/3x = 600 x = 600(3/2) x = 1800/2 x = 900 ===> total poultry 900 - 600 (sold) = 300 poultry were left after day 1