sum of the ages of dad & son is 45. 5yrs ago the product of their age was 34. what is age of dad & son?

Question

please give me the method of solving the following : the sum of the ages of dad & son is 45. 5yrs ago the product of their age was 34. what is the age of dad & son?

Answer 1

let Dad's age be 'd' and son's age be 's'.
so from the given data d+s=45
condition 2: 5 yrs ago age of son =s-5
5 yrs ago age of dad=d-5
given (s-5)*(d-5)=34
by trial error we get the values as 2 and 17,1 and 34
so son is 1yrs and dad is 34 yrs
Finally the Present age of son is 6 and dad is 39 so their sum is 45.

Answer 2

let dad's age be d and son's age be s

sum of their ages is 45

s + d = 45
d = 45 - s...(1)

5 yrs ago product of their ages was 34

(s-5)x(d-5) = 34...(2)

Substituting (1) in (2)

(s-5)x(40-s) = 34
(s-5)(s-40)+34=0
s^2 + 234 - 45s = 0

solve this quadratic equation using determinant method

D = 45^2 - 4x234x1 = 1089
s = 45 +or- sqrt(D)
-------------------
2

s = (45+33)/2 = 39 yrs old
But this makes the dad 6 yrs old which is impossible hence we go for the second solution
s =(45-33)/2 = 6 yrs old

therefore son is 6 yrs old and dad 39 yrs old

Answer 3

Let the son's and the dad's present ages be 's' and 'd'

According to the conditions stated above,
s + d = 45 .......(i)
(s-5)(d-5) = 34 .......(ii)

Substituting d = (45-s) in (ii), we get

(s-5)(45-s-5) = 34

s^2 - 45 s +234 = 0

The solution for this eqn is s = 39 or 6.

Answer :
Dad's present age = 39
Son's present age = 6

Answer 4

trial and error or simultanously

let d be the age of dad and s be the age of son
d+s=45 ---(1)
(d-5)(s-5)=34 ---(2)

from (1), d=45-s ---(3)

subst (3) into (2)
(45-s-5)(s-5)=34
(40-s)(s-5)=34
40s-200-s^2+5s=34
45s-234-s^2=0
s^2-45s+234=0
(s-6)(s-39)=0

hence s=6 or 39
subst both ans to get d age

d=39 or 6

thus dad is 39 years old while son is 6 years old(:

Answer 5

representation: x=dad and y=son
PRESENT: x+y=45....... 5 YRS. AGO: xy=34
formula: x+y = 5+xy
solution: find numbers to enable to get the product of x and y...
34,1 or 17,2
multiply both: 34*1= 34
add 5 years to both factors: 34+5+1+5=45
FINAL ANSWER: 5 YRS. Ago dad was 34 yrs. old and son was 1 yr. old.....NOW: dad is 39 yrs. old and son is 6 yrs.old

Answer 6

let the age of father and son be x and y
x+y=45 ..........eqn 1
5 yrs ago
(x-5)(y-5)=34 .......eqn 2
sub eqn 2 in eqn 1
(40-y)(y-5)=34
y*y-45y+234=0
solving this y=6,then sub in eqn 1,x=39
another method product of two ages is 34 which have only two options 17,2 &34,1.From this we can find easily.But first is the universal method while the second is just a short cut method.

Answer 7

D+A = 35
(D-5)(A-5) = 34

DA -5A -5D = 34
DA = 34+ 5*35 = 209
D = 35-A
(35-A)A=209
35A - A^2 = 209
A^2 -35A +209 = 0

this is a quadratic for the age of the son or dad

Answer 8

d + s = 45.5
(d-5) x (s-5) =34

So you have two equations and two unknowns.

Rearranging the first equation gives s=45.5-d
Substituting in the second equation gives....

(d-5) x (45.5-d-5) = 34

(d-5) x (40.5-d) = 34

-202.5 -d^2+5d-40.5d = 34

Solve this quadratic equation and choose the positive solution for d. When you know d you can find s by putting the value of d in any of the equations.

use the formula -b plus or minus the square root of blah blah blah. to solve the quadratic equation.

You do the rest and I'll get back to my job!

Answer 9

33 dad $ 12 son

Answer 10

i've got faith it unquestionably relies upon on the youngster. some have reached a point of adulthood at age 7 or 8 whilst others nonetheless choose a good company reminder of spanking at age 13. i for my section will maximum probable supply up spanking as quickly as my infants get into middle college through fact by using then i've got faith that they'd be getting slightly previous for a toddler's correction. At that factor i could start up applying strategies like grounding them, loss of privileges and hard love (allowing them to make errors to benefit from). this is ultimately as much as you and your husband as to once you establish to end applying spanking, yet i could say around 11 or so could be a good age to flow directly to greater person effects for his or her correction and discipline. *each and every person who's purely coming back with "you mustn't spank interior the 1st place", the asker has made it especially sparkling that she is a supporter of spanking. How approximately letting others who're supporters and can supply her smart solutions cope with it? If all you will do it take a seat there and tell her she's lazy, abusive or what have you ever it may be greater advantageous served someplace else with somebody who has not of course made up their minds with reference to the situation or maybe then the call calling isn't precisely person-like in any case. i be attentive to your opinions are yours to have, yet this asker already made it sparkling that your opinions at the instant are not likely to alter her perspectives. opinions are large, in spite of the incontrovertible fact that once you be attentive to that your opinion would not be triumphant to a particular question then how approximately purely leaving or not this is?