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Let
Home sold for = $x

5% of x = 43150
5/100 (x) = 43150
5x/100=43150
x/20=43150
x=43150*20
x=863000
Home Sold for $863000

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Cost = $109.99
Sales Tax = 109.99 * 7% = 109.99 * 7/100 = 1.0999 * 7 = 7.6993 = $7.70
Total Cost = Sales Tax + Cost = 7.70+109.99= $117.69

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Let
Present age of Mr. Jacob = j
Present age of Son = s

Mr.Jacobs is 4 times as old as his son.
j=4s............(1)
Five years ago,
Mr. Jacob's age = j-5
Son's age = s-5
Then,he was 9 times as old as his son.
j-5=9(s-5)
j-5=9s-45
j=9s-45+5
j=9s-40............(2)
Put the value of j from (1) to (2)
4s=9s-40
4s-9s=-40
-5s=-40
-5s/-5=-40/-5
s=8
Put the value of s in (1)
j=4s
j=4(8)
j=32

Present age of Mr. Jacob = j = 32 years old
Present age of Son = s = 8 years old

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=
=
Taking LCM or LCD
=
=
=
=

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Distance between two points =
Points (-3,2) and (1,-1)

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(5 + 3) • 4
=8*4
=32

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if x = 5, y = 8, and z = 2.
=x+(y*z)
=5+(8*2)
=5+16
=21

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=
=
=
=

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Let
Present age of Deanna = d
Present age of Borther = b

Deanna is twice as old as her brother.
d=2b .......(1)
The difference in their ages is 7 years
d-b=7..........(2)
Plug in the value of d from (1) to (2)
2b-b=7
b=7
Plug in the value of b in (1)
d=2b
d=2*7
d=14
Deanna is 14 and her brother is 7 years old

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(-4,3) and (3,-1)
Distance between two points =

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I f






Then
=?

=
Plug in the value of x in above equation.
=
=
=
=
=

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Sales tax = x
Cost of Commodity = c
Tax% = t
Sales tax = Cost of Commodity * tax%
x= c * t
x=ct (Required Algebraic expression)
Check
=====
Sales tax = x = ?
Cost of Commodity = c = 850
Tax% = t = 6.5%
x=ct
x=850 * 6.5%
x=850*(6.5/100)
x=850*0.065
x=55.25
Sales tax on the motorcycle = $ 55.25

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or
or
or
or

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Let
Ist Integer = x
2nd Integer = x+1






Use














or

or

or
inadmissible


Ist Integer = x = 9
2nd Integer = x+1 = 9+1 = 10

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points (5, 3) and (8, 10)
Slope = rise in y / rise in x
slope = y2-y1/x2-x1
Slope =10-3/8-5
Slope = 7/3

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Slope = rise in y / rise in x
slope = y2-y1 / x2-x1
Points (-3,5) and (7,10)
slope = (10-5)/(7-(-3))
slope = (10-5)/(7+3)
slope = 5/10
slope = 1/2

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Sales tax=75 * 10%
Sales tax=75 * 10/100
Sales tax=75 * 1/10
Sales tax=75/10
Sales tax=7.5
She paid = tax+original price = 7.5+75 = $82.5

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Let
Present age of ancient one = a
Present age of youngste = b

The ancient one is 40 years older than the youngster
a=b+40..........(1)

10 years ago,
age of ancient one was = a-10
age of youngste was = b-10
Then,the age of the ancient one was 22 years greater than seven times the age of youngster
a-10=7(b-10)+22
a-10=7b-70+22
a=7b-70+22+10
a=7b-70+32
a=7b-38..........(2)
Put the value of a from (1) to (2)
b+40=7b-38
b-7b=-38-40
-6b=-78
-6b/-6=-78/-6
b=-78/-6
b=13
put the value of b (1)
a=b+40
a=13 + 40
a=53
Present age of ancient one = a = 53 years old
Present age of youngste = b = 13 years old

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Height=h=?
Area of Triangle = (base*height)/2

Put the values of A and b

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Let
Present age of Sister = s
Present age of Eldest brother = a
Present age of younger brother = b
Present age of youngest brother = c


At present the sister's age is equal to the sum of her brothers' ages.
s=a+b+c...................(1)

Five years ago
age of Eldest brother was = a-5
age of younger brother was = b-5
age of youngest brother was = c-5
Then
the sum of the brothers' ages was half the sister's present age
s/2=a-5+b-5+c-5
s/2=a+b+c-15
s =2(a+b+c-15).........(2)
Put the value of a+b+c from (1) to (2)
s = 2(s-15)
s=2s-30
s=30

And the eldest brother was 4 times as old as the youngest
a-5=4(c-5)
a-5=4c-20
a=4c-15.................(3)


Since their ages are equally spaced sum of ages of eldest brother and youngest brother divide by 2 will be equal to the age of younger brother
b=(a+c)/2
2b=a+c...................(4)

Put the value of 's' and (a+c) in equation (1)
s=a+b+c
s=(a+c)+b
30=2b+b
30=3b
30/3=3b/3
10=b
b=10

Now again put the value of 'b' and 's' in equation (1)
30=a+10+c
30-10=a+c
20=a+c
20-c=a
a=20-c...........(5)

Put the value of 'a' from (5) to (3)
20-c=4c-15
-c-4c=-15-20
-5c=-35
-5c/-5=-35/-5
c=7
Put the value of 'c' in (3)
a=4c-15
a=4(7)-15
a=28-15
a=13


Present age of Sister = s = 30 years old
Present age of Eldest brother = a = 13 years old
Present age of younger brother = b = 10 years old
Present age of youngest brother = c = 7 years old
Check
======

13+10+7= 30 (which is present age of sister)

5 years back
============
age of Eldest brother was = a-5 = 13-5= 8
age of younger brother was = b-5 = 10- 5 = 5
age of youngest brother was = c-5 = 7-5 = 2
8+5+2 = 15 (which is half of the present age of sister)
And the eldest brother was 4 times as old as the youngest
Eldest brother was 8 which is 4 times of 2.

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Let
Present age of Leticia = l
Present age of Kate = k

Leticia is 21 years older than Kate
l=k+21................(1)

In 2 years,
Leticia's age will be = l + 2
Kate's age will be = k + 2
Then,
Leticia will be twice as old as Kate.
l + 2 = 2 (k + 2)
l + 2 = 2k + 4
l = 2k + 4 - 2
l = 2k + 2 ..................(2)
Put the value of l from (1) to (2)
k + 21 = 2k + 2
k - 2k = 2 - 21
-k = -19
Multiply by -1 both sides
k = 19
Put the value of k in (1)
l=k+21
l=19+21
l = 40

Present age of Leticia = l = 40 years old
Present age of Kate = k = 19 years old

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Write an equation to solve this: If my age is 44 and my sisters age is 48 what age will we each be when our total combined age is 150?
Let
Total Combined age will be 150 after = x years

After x years
Your age = 44+x
Your sister's age = 48+x

Sum of ages
44+x+48+x=150
2x+92=150
2x=150-92
2x=58
2x/2=58/2
x=29
After 29 years total combined age will be 150
Your age = 44+x = 44+29 = 73
Your sister's age = 48+x = 48+29 = 77
Your age + Your sisters age = 150
73+77=150
150=150

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Let
Present age of Father = f
Present age of Daughter = d
4 years ago
Age of father = f-4
Age of daughter = d-4
Then
The father was 8 times older than his daughter
f-4=8(d-4)
f-4=8d-32
f=8d-32+4
f=8d-28......................(1)

In twenty years time
Age of father will be = f + 20
Age of daughter will be = d+ 20
Then
father will be twice the age of the daughter.
f+20=2(d+20)
f+20=2d+40
f=2d+40-20
f=2d+20.......................(2)

Plug in the value of f from (1) to (2)
8d-28=2d+20
8d-2d=20+28
6d=48
6d/6=48/6
d=8
Put the value of d in (1)
f=8d-28
f=8(8)-28
f=64-28
f=36


Present age of Father = f = 36 years old
Present age of Daughter = d = 8 years old
Daughter will be 38 years old after 30 years.

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Given
Point (x, y)=(3,-6)
Line: 4x+9y=7
Rearrange the equation according to equation of standard form
4x+9y=7
9y=-4x+7
9y/9=(-4x+7)/9
y=(-4/9)x+7/9
Compare above equation with the equation of line slope-intercept form
y=mx+b
m=-4/9 and b=7/9
Slope of the given line m =-4/9 and y-intercept = b =7/9
Since required line is perpendicular, the multiplication of the slopes of both lines result in (-1), therefore the slope of the required line will be (9/4)
================================================================
Now we have a point (3,-6) and slope (9/4) of the required line we can easily find the required line put these values in the equation of slope-intercept form to find the y-intercept of the required line
y=mx+b
-6=(9/4)(3)+b
-6=27/4+b
-6-27/4=b
-24-27/4=b
-51/4=b
b=-51/4
y-intercept of the required line =b=-51/4
================================================================
Put the values of ‘m’ and ‘b’ in equation of the line slope-intercept form
y=mx+b
y=(9/4)x-51/4
Above equation is the required equation of the line
Red Line = y =(-4/9)x+7/9
Green Line = y =(9/4)x-51/4

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10x+6y=-60
6y=-60-10x
6y/6=(-60-10x)/6
y=(-60/6)-(10x/6)
y=-(5/3)x-10
y=-5x/3-10

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Effective Speed = 100 + 80 = 180 kmph
Distance apart = 100 km
Time = Distance / Speed
Time = 100 / 180
Time = 0.556 hour

After 0.556 hour they will be (approximately)100 kilometers apart.


Check
=====
Mr. Anders will cover = Speed * time = 100*0.556= 55.60 km
Mr. Rich will cover = Speed * time = 80 * 0.556 = 44.48 km
After 0.556 hour they will be = 100.08 miles apart.

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Effective Speed = 540+720 = 1260 mph
Distance = 1890 miles
Time = Distance / Speed
Time = 1890/1260
time = 1.5 hour.

After 1.5 hours two planes will be 1890 miles apart?


Check
======
Plane A Data
============
Speed = 540 mph
Time = 1.5 hour
Distance covered = ?
Distance = Speed * Time
Distance covered= 540 * 1.5 = 810 miles

Plane B Data
============
Speed = 720 mph
Time = 1.5 hour
Distance covered = ?
Distance = Speed * Time
Distance covered = 720 * 1.5 = 1080 miles

Total Distance between two planes after 1.5 hours = 1080+810 = 1890 miles