Problem Solving - algebraic equations: please help!!!!!!!!?

Question

And could you explain the steps? Thanks
1)In 5 years time i will be 4 times as old as my son. In 11 years time, the sum of ages will be 62. Find the sum of our ages today, find how old I am and my son today.

2) In four years time a mother will be three times as old as her son. Four years ago she was five times as old as her son. Find their present ages.

Answer 1

1. Let my age is x and my son's age is y as of now. After 5 years, the eqn is going to be

x+5=4(y+5)

i.e x=4y+15 -> Eqn A

In 11 years, the eqn is

(x+11)+(y+11)=62

i.e x+y = 40 -> Eqn B

If you solve the above two eqns

YOu will get x=35 and y = 5

2. The eqns are

x+4=3(y+4) -> x = 3y+8

x-4=5(y-4) -> x = 5y - 16

If you solve them you will get x=44 and y=12

Answer 2

Let
m = age of mother now
s = age of son now

1) In 5 years time i will be 4 times as old as my son. In 11 years time, the sum of ages will be 62. Find the sum of our ages today, find how old I am and my son today.

m + 5 = 4(s + 5)
(m + 11) + (s + 11) = 62

m + s + 22 = 62
m + s = 40

m + 5 = 4(s + 5)
m = 40 - s
40 - s + 5 = 4s + 20
25 = 5s
s = 5
m = 40 - s = 40 - 5 = 35

The ages of the mother and son today are 35 years old and 5 years old. The sum of their ages today is 40.
________________

2) In four years time a mother will be three times as old as her son. Four years ago she was five times as old as her son. Find their present ages.

m + 4 = 3(s + 4)
m - 4 = 5(s - 4)

2m = 3(s + 4) + 5(s - 4) = 3s + 12 + 5s - 20 = 8s - 8
m = 4s - 4

m + 4 = 3(s + 4)
4s - 4 + 4 = 3s + 12
s = 12
m = 4s - 4 = 4*12 - 4 = 48 - 4 = 44

Today the mother is 44 and the son is 12.

Answer 3

1) Let x be the son's age in 5 years. Then, we make a chart.

. . . . Age now . . . . . . . Age in 5 years . . . . . . . Age in 11 years time

Son: x - 5 . . . . . . . . . . . . . . . x . . . . . . . . . . . . . . . . . x + 6
Me: 4x - 5. .. . . . . . . . . . . . . .4x . . . . . . . . . . . . . . . . 4x + 6

In 11 years time, the sum of the son and my age will be 62. Therefore,

x + 6 + 4x + 6 = 62
5x + 12 = 62
5x = 50, so x = 10

Since we want to know how old my son and I are today, we consult the chart.
Son's age: x - 5, so since x = 10, 10 - 5 = 5
My age: 4x - 5. If x = 10, then 4(10) - 5 = 40 - 5 = 35.

Answer 4

1.let father's age be y
let son's age be x
by given data, 4x+5=y+5
(x+11)+(y+11)=62
by solving these equations we get x=5 and y=35.
sum of the ages=5+35=40
ur age is 35 and ur son's is 5

2.let mother's age be x
let son's age be y
by given data,x+4=3(y+4)
x-4=5(y-4)
by solving these euations we get x=44,y=12
the present ages of mother and son are 44 and 12 respectively.Got it!

Answer 5

usually with algebraic equations for every unknown factor they will give you one piece of information. Use it.

in this case info are
-5 years time I will be 4 times as old as my son
-11 years time the sum of our ages will be 62

let F = father, S = son
1. F+5 = 4(S+5)
2. F+S+11 = 62

from there solve simultaeneous equations. Same with the question (2)

let M = Mum and S = Son
four years mum is three times as old as the son
-M+4 = 3(S+4)

four years ago she was five times as old as her son
-M-4 = 5(S-4)

solve the two simulatenously.

Answer 6

well the answer to the first question is
dad =x
son =y
hence
x+5=4(y+5)
and
(x+11)+(y+11)=62
y=40-x
putting this value of y in first equation we get
x+5=4[(40-x)+5]
x=35
y=5
dad is 35 years old today and son is 5 years old

solution to 2nd prob
x+4=3(y+4)
x-4=5(y-4)

x=42.5
y=11.5

Answer 7

1. your age is M, your son's age is S

(M+5)/4=(S+5)

(M+11)+(S+11)=62


solve that system


2. M=mother's age, S= son's age

(M+4)/3=(S+4)

(M-4)/5=(S-4)

Answer 8

1)father and son

suppose x is your age today and y is your son's age!
then
x+5=(y+5)*4 (1)
(x+11)+(y+11)=62 (2)
From (1)
x=4y+15 (3)
From (2)
x+y=40 (4)

(3)->(4)
4y+15+y=40
5y=25
y=5
and x=4*5+15=35

so your age today is 35 and son's age today is 5

2)mother and son
suppose x is mother's age today and y is son's age today
then
x+4=(y+4)*3 (1)
x-4=(y-4)*5 (2)

From (1)
x=3y+8 (3)
From (2)
x=5y-16 (4)
(4)-(3)
x=5y-16
-) x=3y+8
--------------------------
0=2y-24
y=12
and x=3*12+8=44

so mother's age today is 44 and son's age today is 12

Answer 9

enable x be the form of goodies peter supplies so now peter could have 25 - x and Lilian could have fifty 5 + x so now lilian has 4 cases greater advantageous than peter so 4(25 - x) = fifty 5 + x one hundred - 4x = fifty 5 + x 5x = 40 5 x = 9

Answer 10

01.

Assume your and your son's current age is x and y respectively.
In5 years time equation will be
x+5 = 4(y+5)
=> x - 4y = 15 -------------------------------------------------------equ 1
In 11 years time
(x+11) +(y+11) = 62
=> x + y = 40 - -------------------------------------------------------equ 2

subtract equ1 from equ2
(x + y) - (x - 4y) = 40 - 15
=> 5 y = 25
therefore y = 5
place value of y in equ 2
x + 5 = 40
hence x = 35

Answer
sum of your age x+y = 40
Your current age x = 35
Your son current age y = 5


02

Assume mother and her son current age is x and y respectively.
In 4 years time equation will be
x+4 = 3(y+4)
=> x - 3y = 8 -------------------------------------------------------equ 1
4 years ago
(x-4) = 5(y-4)
=> x - 5y = -16 - -------------------------------------------------------equ 2

subtract equ1 from equ2
(x - 5y) - (x - 3y) = -16 - 8
=> -2 y = -24
therefore y = 12
place value of y in equ 2
x - 5*12 = -16
hence x = 44

Answer
Mother current age x = 44
Her son current age y = 12