In three years time a dog will be as old as his owner was five years ago.Their present ages total 22 years.Find the age of each using simultaneous equations
age of dog ---- x
age of owner --- y
x + y = 22 or y = 22-x
age of dog 3 years from now: x + 3
age of owner 5 years ago : y - 5
x + 3 = y - 5
x + 3 = 22-x - 5
2x = 14
x = 7 , and y = 22-7 = 15
or the two equations were:
x + y = 22
x - y = -8
add them ..
2x = 14 , just as before
Thank u for the answer
Why did the dog bring a calculator to the party?
Because he knew there would be a lot of addition and subtraction!
Let's solve this age puzzle using simultaneous equations. Let the present age of the owner be O, and the present age of the dog be D.
According to the information given, "In three years time, a dog will be as old as his owner was five years ago." This can be represented as:
(D + 3) = (O - 5)
The second piece of information states that their present ages total 22 years:
O + D = 22
Now, let's solve these equations to find their ages.
From the first equation, we can rewrite it as:
D = (O - 5) - 3
D = O - 8
Substituting this expression for D into the second equation:
O + (O - 8) = 22
2O - 8 = 22
2O = 30
O = 15
Plugging this value of O back into the second equation:
15 + D = 22
D = 22 - 15
D = 7
So, the owner is 15 years old, and the dog is 7 years old. Ta-da!
Let's assume the current age of the dog is D and the current age of the owner is O.
According to the given information, in three years time, the dog will be (D + 3) years old, and the owner was (O - 5) years old five years ago.
We can set up two equations based on the given information:
1) In three years time, the dog will be as old as his owner was five years ago:
D + 3 = O - 5
2) The sum of their present ages is 22 years:
D + O = 22
Now we have a system of two equations with two variables. We can solve it using simultaneous equations.
From equation 1, we can rearrange it to express D in terms of O:
D = O - 8
Substituting this value into equation 2:
(O - 8) + O = 22
2O - 8 = 22
2O = 22 + 8
2O = 30
O = 30/2
O = 15
Now we can substitute the value of O back into equation 2 to find the value of D:
D + 15 = 22
D = 22 - 15
D = 7
Therefore, the current age of the dog is 7 years and the current age of the owner is 15 years.
To find the ages of the dog and its owner, we can set up two equations using simultaneous equations.
Let's assume:
- The present age of the dog is D years.
- The present age of the owner is O years.
Equation 1: "In three years time, the dog will be as old as his owner was five years ago."
After three years, the dog's age will be D + 3.
The owner's age five years ago would be O - 5.
We can now write the equation as:
D + 3 = O - 5
Equation 2: "Their present ages total 22 years."
The dog's present age is D, and the owner's present age is O.
So, we can write the equation as:
D + O = 22
We have a system of two equations, and we can solve it using simultaneous equations.
To do this, let's solve Equation 1 for D:
D = O - 5 - 3
D = O - 8
Now substitute the value of D in Equation 2:
(O - 8) + O = 22
2O - 8 = 22
2O = 22 + 8
2O = 30
O = 30/2
O = 15
Now substitute the value of O in Equation 2 to find D:
D + 15 = 22
D = 22 - 15
D = 7
Therefore, the dog is 7 years old and the owner is 15 years old.