Question 1157116: 1. The sum of two numbers is 30. Five times the smaller exceeds twice the larger by 17. Find the numbers.
2. Tim is 1/5 as old as Tom. In six years, Tim will be 1/3 as old. Find their present ages.
3. A man invested part of $15,000 at 12% and the remainder at 8%. If his annual income from the two investments is $1456, how much does he have invested at each rate?
4. How many gallons of cottonseed oil must be added to 45 gallons of a solution of olive oil, which is 90% olive oil, in order to make the resulting solution 80% olive oil?
5. Tea worth $4.10 per pound is to be mixed with tea worth $4.90 per pound. How many pounds of each should be used to obtain 25 lb. of a blend worth $4.40 per pound?
i hope you can help me for this... although my teacher gave me a sample but i can't understand... thank you :)
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! 1. The sum of two numbers is 30. Five times the smaller exceeds twice the larger by 17. Find the numbers.
Smaller number = x
Larger number = 30 - x
5x = 2(30 - x) + 17
5x = 60 - 2x + 17
5x = 77 - 2x
7x = 77
x = 11
Smaller number = x = 11
Larger number = 30 - x = 30 - 11 = 19
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2. Tim is 1/5 as old as Tom. In six years, Tim will be 1/3 as old. Find their present ages.
Tom's age = x
Tim's age = x/5
(x + 6)/3 = x/5 + 6
x/3 + 2 = x/5 + 6
x/3 - x/5 = 4
5x/15 - 3x/15 = 4
2x/15 = 4
2x = 60
x = 30
Tom's age = x = 30
Tim's age = x/5 = 30/5 = 6
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3. A man invested part of $15,000 at 12% and the remainder at 8%. If his annual income from the two investments is $1456, how much does he have invested at each rate?
12% rate
Principal = p
Rate = 0.12
Interest = 0.12p
8% rate
Principal = 15000 - p
Rate = 0.08
Interest = 0.08(15000 - p) = 1200 - 0.08p
0.12p + (1200 - 0.08p) = 1456
0.12p + 1200 - 0.08p = 1456
0.04p = 256
p = 6400
12% rate
Principal = p = $6400
8% rate
Principal = 15000 - p = 15000 - 6400 = $8600
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4. How many gallons of cottonseed oil must be added to 45 gallons of a solution of olive oil, which is 90% olive oil, in order to make the resulting solution 80% olive oil?
 = 0.80
 = 0.80
0.80(45 + x) = 40.5
36 + 0.80x = 40.5
0.80x = 4.5
x = 5.625
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5. Tea worth $4.10 per pound is to be mixed with tea worth $4.90 per pound. How many pounds of each should be used to obtain 25 lb. of a blend worth $4.40 per pound?
Pounds of $4.10 tea = x
Pounds of $4.90 tea = y
x + y = 25
4.10x + 4.90y = 25(4.40)
x + y = 25
4.10x + 4.90y = 110
Multiply first equation by -4.90:
-4.90x - 4.90y = -122.50
4.10x + 4.90y = 110
Add both equations together:
-0.80x = -12.50
x = 15.625
We now know x = 15.625. To find y, we simply plug that into:
x + y = 25
15.625 + y = 25
y = 9.375
Pounds of $4.10 tea = x = 15.625
Pounds of $4.90 tea = y = 9.375
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