Word problems....?

. Flying with the wind, a plane flew 1800 mi. in 3 hours. Against the wind, the plane required 5 hours to fly the same distance. Find the rate of the plane in calm air.

A merchant mixed 30 lb. of peanuts with 20 lb. of cashews. The 50-lb. mixture sells for $203. S scond mixture included 40 lb. of peanuts and 60 lb. of cashews. the 100-lb mixture sells for $484. Find the cost per pound of the cashews.

An investment of $6000 is made at an annual simple interest rate of 4.2%. How much additional money must be invested at an annual simple interest rate of 8.5% so that the total interest earned is 6% of the total investment?

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  • alpha
    Lv 7
    1 decade ago
    Favorite Answer

    Let tje s[eed pf tje plane be x mph and the calm air and let the sped of the wind be y mph

    by the problem,

    x+y=1800/3=600......(1)

    x-y= 1800/5=360.......(2)

    Adding eqn. nos. 1 and 2,we get

    2x=960=>x=480

    Therefore,the sped of the plane in calm air is 480 mph

    Let the cost of peanut be $x per pound and that of the cashew be $y per pound

    According to the proble,

    30x+20y=203.....(1)

    40x+60y=484....(2)

    Multiplying eqn 1 by 4 and eqn 2 by 3,we get

    120x+80y=812

    120x+180y=1452

    (subtracting) -100y=-640

    Henc,y=640/100=6.40

    Putting the value of y in eqn.1

    30x=203-20*6.40

    x=2.5

    Therefore,the cost of peanuts and cashewnuts are $2.50 and $6.40 per pound respectively

    Let us assume that an amount of$x must be invested @8.5%

    Annual interest of $6000 @4.2%

    =$6000*0.0.42=$252

    Annual interest of $6000+x @6%

    =0..006(6000+x)

    =360+0.06x

    And the amount of interest of$x @8.5%

    =0.085x

    Hence by the problem.

    252+0.085x=360+0.06x

    =>0.025x=108

    x=108/0.025

    =4320

    Hence $4320 nore is to be invested at 6.5%

    Source(s): Experience of 50 years
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  • Anonymous
    1 decade ago

    the 1st

    divide by 3 (because it took 3 hours)

    x (speed of plane)+y(speed of wind)= 1800/3 =600miles

    devide by 5

    x - y = 1800/5 = 360

    now add the 2 together

    2x = 360+600 =960.

    Divide by 2

    x = 480 miles per hour

    Now it's time to substitute

    480 + y = 600

    Transpost the terms

    y = 600 - 480

    Combine the terms

    y = 120 miled per hour

    Time to check

    480 + 120 = 600 (it checks)

    480 - 120 = 360 (it checks)

    the answer id 480 miles per hour

    Source(s): me
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  • 1 decade ago

    rate * time = distance

    rate of plane: x

    rate of wind: y

    with the wind:

    rate = x + y

    time = 3

    distance = 1800

    against the wind:

    rate = x - y

    time = 5

    distance = 1800

    3(x + y) = 1800 ---> x + y = 600

    5(x - y) = 1800 ---> x - y = 360

    add the two equations together:

    2x = 960

    x = 480

    -------------------------

    30p + 20c = 203 (#1)

    40p + 60c = 484 (#2)

    multiply #1 by -4: -120p - 80c = -812

    multiply #2 by 3: 120p + 180c = 1452

    add them together:

    100c = 640

    c = 6.4

    ---------------------------

    6000(0.042) + x(0.085) = (6000+x)(0.06)

    252 + (0.085)x = 360 + (0.06)x

    (0.085)x = 108 + (0.06)x

    (0.025)x = 108

    x = 4320

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  • 1 decade ago

    #1- 60 mph.

    #2- $10.15

    #3- didn't try

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  • 1 decade ago

    450 mph

    30x+20y=203

    40x+60y=484

    ~~~~~~~~~~~

    -90x-60y=-609

    40x+60y=484

    -50x=-125

    x=2.50

    40(2.50)+60y=484

    100+60y=484

    60y=384

    y=6.40

    Peanuts=$2.50

    Cashews=$6.40

    ~~~~~~~~~~~~~~~~``

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