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1500 is divided into three parts, 1/2 of the first part is same
as 1/3rd of the second and
3/5th of third.
find each part
:
"1500 is divided into three parts,"
a + b + c = 1500
:
"1/2 of the first part is same as 1/3rd of the second"
a = b
multiply by 3
a = b
:
"and 3/5th of third. find each part"
a = c
multiply by (5/3)
a = c
:
replace b and c in the total equation
a + a + a = 1500
multiply by 6, results
6a + 3(3a) + 5a = 6(1500)
6a + 9a + 5a = 9000
20a = 9000
a = 9000/20
a = 450 is the 1st part
then
b = *450
b = 675 is the 2nd part
and
c = *450
c = 375 is the 3rd part
:
:
See if that adds up: 450 + 675 + 375 = 1500

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An automobile car traveled 200 miles and at same time
a truck can travel 150 miles .
If the automobile travels at the average speed of 15 miles per hour faster
than the truck then .
Find their average rate?
:
Let s = speed of the truck
then
(s+15) = speed of the car
;
Write a time equation: time = dist/speed
:
truck time = car time
=
Cross multiply
150(s+15) = 200s
150s = 2250 = 200s
2250 = 200s - 150s
2250 = 50s
s = 2250/50
s = 45 mph is the speed of the truck
then
45 + 15 = 60 mph is the speed of the car
:
:
Confirm this by finding the time of each, they should be equal
150/45 = 3.33 hrs
200/60 = 3.33 hrs

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let x = the 10's digit
let y = the units
then
10x+y = "the number"
and
10y+x = "the number reversed
:
write an equation for each statement
:
"nine times a two digit number is the same as twice the number obtained on
interchanging the digits of the number."
9(10x+y) = 2(10y+x)
90x + 9y = 20y + 2x
90x - 2x = 20y - 9y
88x = 11y
simplify, divide by 11
8x = y
;
"If one digit of the number exceeds the other by 7,"
y = x + 7 (y has to be the larger number)
replace y with 8x
8x = x + 7
8x - x = 7
7x = 7
x = 1
then
y = 8
:
18 is the original number
:
:
Check this in the 1st statement
9(18) = 2(81)

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a car travels 255 miles in 3 hours and 45 minutes.
how many miles does it travel per hour?
:
Change time to 3.75 hrs
:
speed = dist/time
:
s =
s = 68 mph

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A rectangular garden is 60 ft by 80 ft.
Part of the garden is torn up to install a sidewalk of uniform width around the garden.
The new area of the garden is one sixth of the old area.
How wide is the sidewalk?
:
Let x = the width of the walk
:
The new dimensions of the garden will be (60-2x) by (80-2x)
:
Find the original area: 60*80 = 4800 sq/ft
Find the new area: *4800 = 800 sq/ft
:
(60-2x)*(80-2x) = 800
FOIL
4800 - 120x - 160x + 4x^2 = 800
Combine on the left as a quadratic equation
4x^2 - 280x + 4800 - 800 = 0
4x^2 - 280x + 4000 = 0
simplify divide by 4
x^2 - 70x + 1000 = 0
Factors to
(x-20)(x-50) = 0
Two solutions
x = 50, not reasonable
and
x = 20 ft is the width of the walk
:
:
Check this with the new dimensions (2x = 40):
(80-40)*(60-40) = 800 sq/ft

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Train A travels at 90 miles per hour and covers 360 miles.
Train B covers the same distance but travels at 60 miles per hour.
How much longer does it take Train B than Train A to cover that distance?
:
Write a time equation,
t = -

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the problem.
factor in a manner that will will reveal the perfect 4th power values
4th power of 3 is 81 and is also a factor of 486, going into that 6 times
:

extract the 4th root of the perfect 4ths and you have
3*x*x*x*y*y*
which is

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= 341 times

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It's quite apparent if you factor this

Cancel out (x-1)'s and see what you have

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Two trucks left two towns A and B at the same time, and each was headed to
the other town at a constant speed, passing each other at point C.
The truck from town B completed the journey from C to A in 20 minutes.
The truck from A completed the journey from A to C in 45 minutes, while
maintaining its steady speed of 45 km/h.
Find the speed of the truck from B in km/h, assuming that it maintains a constant speed throughout.
:
A <--------<20min<--------C----------------< B; truck from B

A >-------->45min>-------C-----------------> B: truck from A (at 45km/h)
:
Change 20 min to .33 hrs
Change 45 min to .75 hrs
:
Since truck from A completed the distance from A to C in 45 min at 45 km/h,
dist from A to C: .75(45) = 33.75 km
:
Find the speed of truck from B, which traveled from C to A in 20 min:
S = = 101.25 km/hr

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If Mark is traveling South at 10 miles per hour for 45 minutes,
and Sally is traveling North at 5 miles per hour for 30 minutes,
and they meet after one hour, how far apart were they when they began?
:
The distance they were apart will equal the total distance they traveled.
:
Write a distance equation; d = speed * time
:
Change 45 min to .75 hrs, and 30 min to .5 hrs
:
d = 10(.75) + 5(.5)
d = 7.5 + 2.5
d = 10 mi apart
:
Not sure how "they meet after one hour" fits into this

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from an h=63 feet observation tower on the coast, a coast guard sights a boat.
the angle of depression is 4 degrees.
how far is the boat from the shore line?
:
The interior angle of the right triangle formed by tower, the boat and
the shore line: 90 - 4 = 86 degrees
:
The tangent can be used here, side opposite/side adjacent
Let s = distance from the shore to the boat (side opposite 86 degrees)
:
tan(86) =
s = 63 * tan(86)
s = 63 * 14.3
s = 900.94 ft from the shore to the boat

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Mike runs 8 miles per hour. An hour later, Dave leaves for his morning bike
ride traveling the same route as mike.
Dave bikes 20 miles per hour.
How long will mike have been running when Dave catches him?
:
Let t = Mike's running time
then
(t-1) = Dave's travel time (left an hr after Mike)
:
When Dave catches Mike, they will have traveled the same distance.
Write a distance equation: dist = speed * time
:
20(t-1) = 8t
20t - 20 = 8t
20t - 8t = 20
12t = 20
t = 20/12
t = 1 hrs which would be 1 hr 40 min, Mike's running time.
:
:
Check this by finding the dist each traveled, should be equal
Mike: 1.67 * 8 = 13.33 miles
Dave: .67 * 20 = 13.33 miles

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John works two part-time jobs for a total of 25 hours per week.
Job A pays $7.50 per hour and Job B pays $8.40 per hour.
How many hours did he work at each job if he made $200.10 this week?
:
Let a = no. of hrs worked at job A
Let b = no. of hrs worked at job B
:
Write an equation for each statement;
:
"John works two part-time jobs for a total of 25 hours per week."
a + b = 25
a = (25-b); we can use this form for substitution
;
"Job A pays $7.50 per hour and Job B pays $8.40 per hour.he made $200.10"
7.50a + 8.40b = 200.10
replace a with (25-b)
7.50(25-b) + 8.40b = 200.10
187.50 - 7.50b + 8.40b = 200.10
-7.50b + 8.40b = 200.10 - 187.50
.90b = 12.60
b = 12.60/.9
b = 14 hrs on job B
:
I'll let you find job A, ensure the $ add up 200.10

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Twin brothers, person A and person B, can mow their grandparents lawn together in 42 minutes.
Person B takes 13 minutes more than person A.
How long does it take each person to mow alone?
:
let t = time required by A to mow it alone
then
(t+13) = time required by B
Let the completed job = 1 (a mowed lawn)
:
A shared work equation
:
+ = 1
multiply by x(x+13), resulting in eliminating the denominators,
42(x+13) + 42x = x(x+13)
:
42x + 546 + 42x = x^2 + 13x
84x + 546 = x^2 + 13x
0 = x^2 + 13x - 84x - 546
A quadratic equation
x^2 - 71x - 546 = 0
You can use the quadratic formula here, but this will factor
(x+7)(x-78) = 0
the positive solution
x = 78 minutes, A alone
then
78+13 = 91 min. B alone
:
:
See if that works out
on a calc:
42/78 + 42/91 = 1

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e^(x + 3) = 22
Find the nat log of each side
ln(e^x+3)) = ln(22)
log equiv of exponents
(x+3)ln(e) = ln(22)
Find the log, ln of e is 1 so we have
x + 3 = 3.09104
x = 3.09104 - 3
x = .09104
:
:
Check this on you calc
enter e^(.09104+3) results: 21.99999 ~ 22

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A train takes 2 hours to reach station b from station a,
and then 3 hours to return from station b to station a.
The distance between the stations is 200 km.
Find the (a) average speed
let a = average speed, it took 5 hrs to travel 400 km
a =
a = 80 km/hr
:
(b) average velocity of the train.
Velocity involves direction and displacement
Since it ended up in the same place it started (A); velocity is 0

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by how much is a car exceeding the speed limit of 100km/hr if it travels
at 180 kms in 1.5 hours
:
Find the actual speed; speed = dist/time
= 120 km/h
:
You decide how much over the speed limit that is.

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REplace A with proper expression where the fractions are equivalent:
:
=
factor out 7 in the 2nd numerator
=
divide both sides by 7, results:
=
Cross multiply
A = (a+5)(a-5)
A = a^2 - 25
Equiv:
=

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a will states that 3/5 of an estate is to be divided among relatives.
Of the remaining, 1/4 goes to charity. How much goes to charity
:
Remaining will be 2/5
:
* = = to charity

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(x-22)^2 Please solve using square root property
This is not an equation, just an expression, did you mean?
(x-22)^2 = 0
(x-22)(x-22) = 0
solution
x = 22

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√12* √150
:
Factor inside the radicals to reveal perfect squares
*
Extract the square root of those squares
*
Multiply now

factor to reveal a perfect square again, extract the square root of 9
= =

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A turkey takes 6.25 hours to cook and instructions said 15 minutes per pound,
how many pounds was the turkey?
:
change 15 min to hrs: 15/60 = .25 lb
= 25 lb

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1) Little City Air Tran had a passenger reduction and lost 1/6 of its passengers.
If 110 remain after the reduction, how many were there originally?
:
Let x = original number of passengers
They tell you how many REMAIN. If they lost 1/6, then 5/6 remain, right?
therefore
x = 110
multiply by 6
5x = 6(110)
5x = 660
x = 660/5
x = 132 passengers originally
:
:
2)A box contains 37 coins consisting of pennies, dimes, and quarters, the total value is $2.23.
let p = no. of pennies
let d = no. of dimes
let q = no. of quarters
:
The total coin equation
p + d + q = 37
:
the total value equation
.01p + .10d + .25q = 2.23
:
How many pennies (equal to the amount of dimes) are there?
p = d
Replace d with p in the total coin equation, and you have
2p + 1q = 37
Replace d with p in the total value equation, and you have
.11p + .25q = 2.23
Multiply by 4 and subtract
2p + 1q = 37.00
.44p + 1q = 8.92
------------------subtraction eliminates q, find p
1.56p + 0 = 28.08
p =
p = 18 pennies
:
How many quarters are there?
Use the equation 2p + 1q = 37, replace p with 18
2(18) + q = 37
36 + q = 37
q = 37-36
q = 1 quarter
:
See if that adds up (remember we have 18 dimes): .18 + 1.80 + .25 = 2.23
:
:
3) A crew receives a check for $4250 for a job.
A journeyman makes 300% of what an apprentice makes, and a master makes
150% of what a journeyman makes.
:
Let a = amt made by the apprentice
From the given information we can say
j = 3a)
:
m = 1.5(3a)
m = 4.5a
:
a + j + m = 4250
Replace m and j, find a
a + 3a + 4.5a = 4250
8.5a = 4250
a = 4250/8.5
a = $500 made by the apprentice
:
I'm going to let you find the amt made by j and m
Confirm that your values add up 4250
:
:
If your medication prevents you from doing this, change medication or doctors or both!
:
How much does the apprentice make?
How much does the master make?
How much does the journeyman make?

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Will a 36 inch femur bone fit in a 3 inch tall box has a 21 inch square box?
No, not even close.

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What you have is a vertical line, the slope is "undefined"
As you can see
m = = , division by 0

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write it:
n^2 - 25 = 0
add 25 to both sides and you have
n^2 = 25
n =
n = +5
and
n = -5
:
Check replace n with 5:
5^2 - 25 = 0
and
replace n with -5
(-5)^2 - 25 = 0

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Generally, when you replace the unknown (x) with your solution in the original equation, you will have equality (left side value = right side value)

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25 cent - a quarter is 3/4 inch in diameter.
When placed 7 feet from eye, it blocks the disc of moon. Diameter of the moon is 2160 miles. How far is the moon from the earth?
;
Using the rule of similar triangles
:
Convert 7 ft to 84 inches
let d = distance to the moon
:
A ratio equation
=
Cross multiply
.75d = 2160*84
d =
d = 241,920 miles to the moon

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which of the followings sets of numbers could be the lengths of sides of a triangle?
1 mi, 9 mi, 10 mi
or
8 mi, 9 mi, 2 mi
or
1 mi, 9 mi, 11 mi
or
8 mi, 9 mi, 17 mi
:
The rule: "the sum of the two smaller sides has to exceed the longest side"
so only the 2nd one can be a triangle

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): a car engine hold 7 litres of oil, u want to add 10% of engine treatment how much additive do u use
:
Assume you want 10% of the 7 liter mixture to be additive
:
Drain .7 liters of the original oil (if it is full).
Add .7 liters of the additive
:
If you are changing the oil, add 6.3 liters of oil, then .7 liters of additive