Question

please answer 68,69,70,71,72

Solve the problem using a system of equations. 68) Paul invested three times as much money in an account paving 7% interest than he did in an account paying 2% Interest. Ir the total interest paid was $920. how much did he invest in each? 68) 69) 69) Chuck and Dana agree to meet in Chicago for the weekend, Chuck travels 180 miles in the same time that Dana travels 165 miles. If Chuck's rate of travel is 3 mph more than Dana's. then at what rate does Chuck travel? 70) Anne and Nancy use a metal alloy that is 12% copper to make jewelry, How many ounces of a 10% alloy must be mixed with a 16% alloy to form 87 ounces of the desired alloy? 70) 71) 71) Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $135.00 for 3 days and 300 miles, while Mary was charged $247.00 for 5 days and 600 miles What does Best Rentals charge per day and per mile? 72) 72) A company sells nuts in bulk quantities. When bought in bulk, peanuts sell for $1.30 per pound, almonds for $2.40 per pound, and cashews for $3.15 per pound. Suppose a specialty shop wants a mixture of 320 pounds that will cost $2.59 per pound. Find the number of pounds of each type of nut if the sum of the number of pounds of almonds and cashews is three times the number of pounds of peanuts. Round your answers to the nearest pound

Answer 1

68. Let the amounts invested by Paul in the accounts paying 2 % and 7 % interest be $ x and $ 3x respectively.

The interest earned by Paul on these accounts, for an year , is 0.02x+0.07*3x = 0.23x.

Hence 0.23x = 920 so that x = 920/0.23 = 4000.

Thus, Paul had invested $ 4000 in the account paying 2 % interest and $ 12000 in the account paying 7 % interest.

69. Let Chuck and Dana travel 180 and 165 miles respectively in x hours. Then their rates of travel are 180/x and 165/x m.p.h. respectively.

Now, we have 180/x = 165/x +3 or, 180/x -165/x = 3 or, 15/x = 3 or, 3x = 15 so that x = 15/3 = 5.

Thus, Chuck travels at 180/5 = 36 m.p.h.

70. Let x ounces of 10 % copper alloy be mixed be y ounces of 16 % copper alloy to make 87 ounces of 12 % copper alloy.

Then x+y = 87…(1) and 0.10x +0.16y = 87*0.12 = 10.44 or, 10x+16y = 1044 or, 5x+8y = 522…(2)

On solving these equations, we get x = 58 and y = 29.

Thus, 58 ounces of 10 % copper alloy should be mixed be 29 ounces of 16 % copper alloy to make 87 ounces of 12 % copper alloy.

71. Let the daily fee chages of Best Rentals be $ x and let their charges per mile be $ y.

Then 3x+300y = 135 or, x+100y = 45…(1) and 5x+600y = 247…(2).

On solving these equations, we get x = 23 and y = 11/50 = 0.22.

Thus, the daily fee chages of Best Rentals are $ 23 and let their charges per mile are $ 0.22.

72. Let x pounds of peanuts, y pounds of almonds and z pounds of cashews be mixed to create the desired mixture of 320 pounds of nuts.

Then x+y+z = 320…(1), 1.30x+2.40y+3.15z = 320*2.59 = 828.80 or, 130x+240y+ 315z = 82880...(2) and y+z= 3x or, 3x-y-z = 0…(3).

The augmented matrix of the above linear system mis A(say)

1	1	1	320
130	240	315	82880
3	-1	-1	0

The RREF of A is

1	0	0	80
0	1	0	208/5
0	0	1	992/5

Thus, x = 80, y = 208/5 = 41.6, say 42 and z = 992/5 = 198.4 , say 198 ( on rounding off to the nearest whole number).

Thus, 80 pounds of peanuts, 42 pounds of almonds and 198 pounds of cashews be mixed to create the desired mixture of 320 pounds of nuts.