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Investment (Interest) and Mixture Problems
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Interest Problems page 198 Simple Interest is interest earned on the principle or original amount. Compound interest is interest earned on the principal and on the interest. Simple Interest I=PRT Interest = principal * rate * time rate=interest rate as a decimal 5%=0.05 time = number of years
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Simple Interest problems A table can be used to make it easier to understand the problem. page 199 Yujung invested $3000, part at 8% and part at 7.5% The total return (interest earned) for one year was $231. How much was invested at each rate. PRT=IPrincipalRateTimeInterest Amount invested at 8% 3000-x0.0811(0.08)(3000-x) Amount invested at 7.5% x0.07511(0.075)(x)
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0.08(3000-x) + 0.075x = 231 The interest from each part of the investment adds up to the total interest. if you multiply each term by 1000 to eliminate the decimals, you get: 240,000 – 80x + 75x = 231,000 5x = 9000, x = 1800 Amount invested at 8%3000-x3000-1800 = $1200 Amount invested at 7.5%x$1800
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Practice Page 200 # 1,2
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Page 200 #1 PrincipalRateTimeInterest = PRT Amount Invested at 12%x0.1210.12x Amount Invested at 10%18750-x0.1010.10(18750-x) 0.12x +0.10(18750-x)=2117 0.12x+1875-0.10x=2117 0.02x+1875=2117 0.02x=242 x=12100 18750-x=6650 Amount invested at 12% = $12100 amount invested at 10% = $6650
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Page 200 #2 0.12x + 0.08x + 240 = 760 0.2x = 520 2x =5200 X = 2600 2600 at 12% and 5600 at 8% PrincipalRateTimeInterest = PRT Amount Invested at 12%x0.1210.12x Amount Invested at 8%x + 30000.0810.08(x+3000)
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Mixture problems page 201 How many liters of a 50% alcohol solution must be added with 80 liters of a 20% alcohol solution to make a 40% alcohol solution? 1.What do we know 2.what do we need to know 3.write equation 4.solve
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% solution Solution % as decimal amount of substance Amount of the total mixture 50%0.50x0.5x 20%0.20800.2(80) 40%0.40Total x+800.40(x+80) Part Total 0.5x + 0.2(80) = 0.40(x+80) 0.5x +16 = 0.4x + 32 0.1x = 16 x=160 We need 160 liters of 50% solution to mix with the 80 liters of 20% solution which will make a 240 liters 40% solution.
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Practice Page 202 # 1 (at top of page) typecostAmount (# of lbs)total 32 cents0.32x0.32x 25 cents0.2535-x0.25(35-x) 30 cents0.30350.30(35) 0.32x + 8.75 -0.25x=10.5 0.07x = 1.75 7x = 175 x=25 We need 25 pounds of 32 cent candy and 10 pounds of 25 cent candy
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나우웍 /Homework /Dormwork/ 열람실웍 page 203-206 # 1-12
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