# 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?

Relevance
• alpha
Lv 7

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
• Anonymous

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

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

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

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

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

#1- 60 mph.

#2- \$10.15

#3- didn't try

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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