Please I need help How many gallons each of 30 alcohol and 5

Please I need help!

How many gallons each of 30% alcohol and 5% alcohol should be mixed to obtain 25 gal of 9% alcohol? Gallons of Solution Gallons of Pure Alcohol Percent (as a decimal) 30%-0.3 5% = 0.05 9% = 25 How many gallons of 30% alcohol should be in the mixture? gal

Solution

Percentage

( as a decimal)

2. Let x liters of pure acid be added to 5 % acid solution to get 95 liters of 88 % solution. Since the total volume of the solution is 95 liters, the volume of 5 % acid solution is 95 - x liters. Then x + ( 95 -x) * 5/100 = 95 * ( 88/100) or, x + 0.05x + 4.75 = 83.6 or, 1.05x = 83.6 - 4.75 = 78.85 so that x = 78.85/1.05 = 75.0952381 = 75.10 ( approx. on rounding off to 2 decimal places) Then 95 - x = 95 - 75.10 = 19.90. Thus 79.10 liters of pure acid has to be mixed with 19.90 liters of 5 % acid solution to get 95 liters of 88 % acid solution.

3. Let $ x be invested at 12 % simple interest and $ y be invested at 6 % simple interest . Then , we have

We have x + y = 5400...(1) and 0.12 x + 0.06 y = 504 or, 12x + 6y = 50400 or 2x + y = 8400... (2)

From the 1st equation , we have x = 5400 - y. On substituting x = 5400 -y in the 2nd equation, we have

2(5400 -y) + y = 8400 or, 10800 - 2y + y = 8400 or, y = 10800 - 8400 = 2400. Then x = 5400 - 2400 = 3000. We can verify th=is result as under:

Interest on $ 3000 @ 12 % simple interest for 1 year = 3000 * 0.12 = $ 360

Interest on $ 2400 @ 6 % simple interest for 1 year = 2400 * 0.06 = $ 144

Then, the total interest on $ 5400 for an year = $ 360 + $ 144 = $ 504

4. Let the speed of the train and the plane be x kph and y kph respectively. Then y = 3x - 10...(1)

Further, since Time = distance/speed, we have 140/x = 392/y or, 392x = 140 y or, 14x = 5y ...(2)

On substituting y = 3x - 10 in the 2nd equation, we get 14x = 5 ( 3x -10) or, 14x = 15x - 50 so that x = 50 and then y = 3x - 10 = 150 - 10 = 140. We can verify this result by computing the time in which the train travels 140 km and the plane travels 392 km. For the train, the time taken to travel 140 km = 140/50 = 2.8 hours.  For the plane, the time taken to travel 392 km = 392/140 = 2.8 hours.

5.

From the above table, we have 2 ( x - y ) = 48 or x - y = 24...(1) and 1.5 ( x + y) = 48 or, x - y = 32...(2). On adding the 2 equations, we have 2x = 24 + 32 = 56 so that x = 28. Then y = x - 24 = 28 - 24 = 4. Thus the rate of the boat in still water is 28 mph and the rate of the current is 4 mph.

6.Let x lbs of candy ( A) selling at $ 0.69 per lb be mixed with candy (B) selling at $ 1.23 per lb to get 7 lb of candy ( C)selling at $ 0.97 per lb. Since, the total weight of the candy C is 7 lb, therefore, the weight of candy B is 7 - x lbs. Then x * 0.69 + ( 7 -x)* 1.23 = 7 * 0.97 or, 69x + 123 ( 7 -x) = 7 *97 or, 69x + 861 - 123x = 679, or, 54x = 861- 679 = 182 so that x = 182/54 = 3.37 ( approximately). The answer is 3.37 lbs.

Gallons of Solution	Percentage ( as a decimal)	Gallons of Pure Alcohol
x	30 % ( 0.30)	0.30x
y	5% ( 0.05)	0.05y
25	9% ( 0.09)	25 * 0.09 = 2.25