Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Math 11 questions!!! help?

The answer is written down. So I am looking for a shown work..

Thanks

1) If a two place # is divided by the sum of its digits the quotient is 8, and the difference between its digits is 5. Find this number..

ANSWER = 72

2) Mac invested $1200, part at 8% and the rest at 6% per year. The interest earned after one year was $88. How much did Mac invest at each rate?

ANSWER = $400 at 6%, 800 at 8%

3) A boat can make a trip up river 60km to a fish camp in 3 hours, and down the river to its starting point in 2hours. If the boat can travel x km/hr in still water and the speed of the current is y km/hr,

Find x and y...

ANSWER: x = 25, y = 5

4) Solve

3a + 4B - c = -2

2a - 3b + c = 4

a - 6b + 2c = 5

ANSWER: (1, -3, -7 )

5) If (a,b,1) is a solution for the system

x + y - 2z = 1

2x - 2y + z= -1

kx - y - z = 2

ANSWER: a= 1, b = 2, k = 5.

Help me answer all the questions.

But if you can answer atleast 1 or 2, please share the shown work =]

Just need it for a review.

Update:

2 & 3 is answered by Lucy << thanks..

Can someone help me with 1, 4, 5?

2 Answers

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  • Lucy
    Lv 7
    1 decade ago
    Favorite Answer

    2) Mac invested $1200, part at 8% and the rest at 6% per year. The interest earned after one year was $88. How much did Mac invest at each rate?

    ANSWER = $400 at 6%, 800 at 8%

    This is a type of mixture problem.

    Hint: Use a table.

    Type ….........………. Qty …………. Interest …………. Total

    8% account …………. x …...………. 0.08 ……....……. x * 0.08 = 0.08x

    6% account …………. y ……...……. 0.06 …....………. y * 0.06 = 0.06y

    Total ………..........…. x + y ………. ----- ……......……. 88

    The first 2 rows of the last column always add up to the third row in that column.

    0.08x + 0.06y = 88

    Given: Combination is 1200 dollars

    Means: x + y = 1200

    You now have 2 equations.

    0.08x + 0.06y = 88

    x + y = 1200

    Solve the 2nd one for x.

    x + y = 1200

    x = 1200 - y

    Replace x with 1200 - y in the 1st one.

    0.08x + 0.06y = 88

    0.08(1200 - y) + 0.06y = 88

    96 - 0.08y + 0.06y = 88

    -0.02y = -8

    y = 400

    Plug this solved y value into x = 1200 - y to solve for x.

    x = 1200 - y

    x = 1200 - 400

    x = 800

    ~~~~~~~~~~~~

    3) A boat can make a trip up river 60km to a fish camp in 3 hours, and down the river to its starting point in 2hours. If the boat can travel x km/hr in still water and the speed of the current is y km/hr,

    Find x and y...

    ANSWER: x = 25, y = 5

    Hint: Use a table.

    ________________ Distance ______________ Rate _____________ Time

    Upstream ________ 60 ___________________ x - y _____________ 3

    Downstream ______ 60 ___________________ x + y ____________ 2

    Remember the distance formula.

    d = rt

    Apply this to what you have.

    ________________ Distance ______________ Rate _____________ Time

    Upstream ________ 60 = 3(x - y) __________ x - y _____________ 3

    Downstream ______ 60 = 2(x + y) __________ x + y ____________ 2

    Your system of equations is:

    60 = 3(x - y)

    60 = 2(x + y)

    Solve the first equation for x.

    60 = 3(x - y)

    60 = 3(x) + 3(-y)

    60 = 3x - 3y

    60 + 3y = 3x - 3y + 3y

    60 + 3y = 3x

    (60 + 3y) / 3 = 3x / 3

    (60 / 3) + (3y / 3) = x

    20 + y = x

    Plug this into the second equation and solve for y.

    60 = 2(x + y)

    60 = 2(20 + y + y)

    60 = 2(20 + 2y)

    60 = 2(20) + 2(2y)

    60 = 40 + 4y

    60 - 40 = 40 + 4y - 4

    20 = 4y

    20 / 4 = 4y / 4

    5 = y

    Plug this back into the modified first equation to find x.

    20 + y = x

    20 + 5 = x

    25 = x

    ANSWER: The speed of the boat in still water is 25 km/h. The speed of the current is 5 km/h.

    Source(s): For more help with mixture word problems: http://www.purplemath.com/modules/mixture.htm For more help with distance word problems: http://www.purplemath.com/modules/distance.htm
  • 1 decade ago

    If you want to do this well figure it out for yourself.

    Source(s): Own experience
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