the sum of the ages of sam and tomas is 27 years. seven years ago, tomas was three years more than one-fourth as old as sam. find their present age
Let Sam's age 7 years ago be s
let Tom's age 7 years ago be t
So
s+7 + t+7 = 27
s+t = 13 ---> t = 13-s
"seven years ago, tomas was three years more than one-fourth as old as sam"
--- t = (1/4)s + 3
13-s = (1/4)s + 3
times 4
52 - 4s = s + 12
-5s = -40
s = 8
so 7 years ago Sam was 8 and Tom was 5
So NOW they are 15 and 12
Check :
is the sum of their present ages 27
15+12 = 27 , check!
7 years ago, is Tom 3 more than 1/4 of Sam's age
1/4 of Sam= 2
3 more than that is 5, which was Tom's age, check!!
Let's assume Sam's current age is "S" and Tomas's current age is "T".
According to the given information, the sum of their ages is 27 years:
S + T = 27 ...(1)
Now, let's consider the second piece of information. Seven years ago, Tomas was three years more than one-fourth as old as Sam:
(T - 7) = (1/4)(S - 7) + 3 ...(2)
To solve these equations, we can use either substitution or elimination method. Let's solve these equations using substitution.
From equation (1), we can express S in terms of T:
S = 27 - T
Now, substitute this value of S in equation (2):
(T - 7) = (1/4)((27 - T) - 7) + 3
Simplify the equation:
T - 7 = (1/4)(20 - T) + 3
T - 7 = 5 - (1/4)T + 3
Combine like terms:
T - (1/4)T = 5 + 3 + 7
(3/4)T = 15
Multiply both sides by 4/3 to isolate T:
T = (15)(4/3)
T = 20
Now, substitute this value of T back into equation (1) to find S:
S + T = 27
S + 20 = 27
S = 27 - 20
S = 7
Therefore, Sam's present age is 7 years and Tomas's present age is 20 years.
To find the present ages of Sam and Tomas, we can set up a system of equations based on the given information.
Let's assume that Sam's present age is represented by S and Tomas' present age is represented by T.
We know that the sum of their ages is 27 years, so we can write the first equation as:
S + T = 27 ...(Equation 1)
Seven years ago, Tomas was three years more than one-fourth as old as Sam. This means if we subtract 7 from Tomas' age and multiply Sam's age by one-fourth (or divide by 4), Tomas' age would be 3 more than that. So, we can write the second equation as:
(T - 7) = (1/4)(S - 7) + 3 ...(Equation 2)
Now, we have a system of equations with two variables (S and T). We can solve this system of equations to find the values of Sam and Tomas' present ages.
To solve this system, we can use the method of substitution or elimination. Let's use the substitution method.
From Equation 1, we can express S in terms of T:
S = 27 - T
Substitute this value of S in Equation 2:
(T - 7) = (1/4)((27 - T) - 7) + 3 ...(Equation 3)
Now, we can simplify and solve this equation for T:
T - 7 = (1/4)(20 - T) + 3
Multiply through by 4 to eliminate the fraction:
4(T - 7) = 20 - T + 12
4T - 28 = 20 - T + 12
Combine like terms:
4T + T = 20 + 12 + 28
5T = 60
Divide both sides by 5:
T = 12
Now that we have found Tomas' present age (T = 12), we can substitute this value back into Equation 1 to find Sam's present age:
S + 12 = 27
S = 27 - 12
S = 15
Therefore, Sam's present age is 15 years and Tomas' present age is 12 years.