The sum of ages of Sam ang thomas is 27 years. Seven years ago, Toma's was three years more than one fourth as old as Sam. Find their present ages
s+t = 27
t-7 = 3+(s-7)/4
...
To find their present ages, let's assign variables:
Let S be the age of Sam.
Let T be the age of Thomas.
We have two equations given:
1. The sum of the ages of Sam and Thomas is 27:
S + T = 27
2. Seven years ago, Thomas's age was three years more than one fourth of Sam's age:
T - 7 = (1/4)(S - 7) + 3
Now, let's solve the equations:
Equation 1: S + T = 27
Equation 2: T - 7 = (1/4)(S - 7) + 3
To solve this system of equations, we can use substitution or elimination method. In this case, let's use the substitution method:
From Equation 1, we can express T in terms of S:
T = 27 - S
Substituting this value of T into Equation 2:
27 - S - 7 = (1/4)(S - 7) + 3
Combine like terms:
20 - S = (1/4)(S - 7) + 3
Next, let's get rid of the fraction by multiplying both sides of the equation by 4 to simplify:
4(20 - S) = 4[(1/4)(S - 7) + 3]
Simplify:
80 - 4S = S - 7 + 12
Combine like terms:
80 - 4S = S + 5
Move all terms containing S to the left side:
80 - 5 = S + 4S
Simplify:
75 = 5S
Divide by 5:
S = 15
Now that we have found the age of Sam to be 15, we can substitute this value back into Equation 1 to find the age of Thomas:
15 + T = 27
T = 27 - 15
T = 12
So, the present age of Sam is 15 years, and the present age of Thomas is 12 years.