sarah, tom and johns were all friiends. sarah and john were surprised to know that tom didn't know how old they were.
sarah: if you add athird of my age to three quartes of toms age you get, 30.5
tom: if you take my age and double it, you get six times the difference of yours and sarahs age.
if john is 34, how old are tom and sarah?
s/3 + 3t/4 = 30.5
2t = 6(j-s)
j=34
solve that and you have
s=24
t=30
To find out the ages of Tom and Sarah, we need to solve the two equations given by Sarah and Tom.
Let's break down the information given:
1. Sarah's statement: If you add a third of my age to three-quarters of Tom's age, you get 30.5.
Let's represent Sarah's age as "S" and Tom's age as "T".
The equation can be written as:
(S + (1/3)S) + (3/4)T = 30.5
(4/3)S + (3/4)T = 30.5
2. Tom's statement: If you take my age and double it, you get six times the difference between your (Tom's) age and Sarah's age.
This equation can be written as:
2T = 6(S - T)
2T = 6S - 6T
8T = 6S
Now, let's use the information that John's age is 34. Since we only need to find Tom and Sarah's ages, we can ignore John's age for now.
We have two equations with two unknowns:
(4/3)S + (3/4)T = 30.5
8T = 6S
To solve the equations, we can use substitution method or elimination method.
Let's use the substitution method:
From the second equation, we can rewrite it as:
S = (8T) / 6
Simplified: S = (4T) / 3
Now substitute the value of S in the first equation:
(4/3)((4T) / 3) + (3/4)T = 30.5
(16/9)T + (3/4)T = 30.5
Now, let's find a common denominator for the fractions:
(64/36)T + (27/36)T = 30.5
(91/36)T = 30.5
To isolate T, we can multiply both sides by 36/91:
T = (30.5 * 36) / 91
T ≈ 12.14
Now, substitute the value of T back into the second equation to find S:
S = (8 * 12.14) / 6
S ≈ 16.23
Therefore, Tom is approximately 12.14 years old, and Sarah is approximately 16.23 years old.