Two yrs ago, Sam was two-thirds of Pam's age ( at that time). In three years, Same will be three-fourths of Pam's age. In 20 yrs, the sum of their ages will be 61. How old is Sam?
Your question is gobble-de-goop
You have 3 conditions imposed on two unknowns, which in this case
leads to a contradiction, as shown when the previous tutor shows that the
solution based on the first two conditions does not satisfy the third condition.
Suppose I solve it based only on the last two conditons:
Let Sam's present age be s, and Pam's current age be p
3 years from now,
Sam will be s+3, and Pam will be p+3
At that time, Sam's age will be three-fourths of Pam's age
---> s+3 = (3/4)(p+3)
4s + 12 = 3p + 9
4s - 3p = -3
third condition: in 20 years, the sum of their ages will be 61
---> s+20 + p+20 = 61
s+p = 21 or p = 21-s
sub into 4s - 3s = -3
4s - 3(21-s) = -3
7s = 60
s = 8.57 , let's say 8 1/2, then Pam is 21-s = appr 12 1/2
different answers, both satisfy your 2nd and your 3rd condition, but not the first.
Check your question!
To solve this problem, we can set up equations based on the given information.
Let's assume Sam's current age is S and Pam's current age is P.
From the first sentence, "Two years ago, Sam was two-thirds of Pam's age (at that time)," we can conclude:
(S - 2) = (2/3)(P - 2) ---- Equation 1
From the second sentence, "In three years, Sam will be three-fourths of Pam's age," we can conclude:
(S + 3) = (3/4)(P + 3) ---- Equation 2
From the third sentence, "In 20 years, the sum of their ages will be 61," we can conclude:
(S + 20) + (P + 20) = 61 ---- Equation 3
Now, let's solve these equations simultaneously to find the values of S and P.
Simplifying Equation 1:
S - 2 = (2/3)(P - 2)
Multiplying both sides of the equation by 3 to eliminate the fraction:
3(S - 2) = 2(P - 2)
3S - 6 = 2P - 4
3S = 2P + 2 ---- Equation 4
Simplifying Equation 2:
S + 3 = (3/4)(P + 3)
Multiplying both sides of the equation by 4 to eliminate the fraction:
4(S + 3) = 3(P + 3)
4S + 12 = 3P + 9
4S = 3P - 3 ---- Equation 5
Simplifying Equation 3:
S + 20 + P + 20 = 61
S + P + 40 = 61
S + P = 61 - 40
S + P = 21 ---- Equation 6
To solve for S, we will substitute equation 6 into equations 4 and 5.
Substituting Equation 6 into Equation 4:
3S = 2P + 2
3S = 2(21 - S) + 2 [Substituted S + P = 21]
3S = 42 - 2S + 2
3S + 2S = 44
5S = 44
S = 44/5
S = 8.8
Substituting Equation 6 into Equation 5:
4S = 3P - 3
4(8.8) = 3P - 3 [Substituted S + P = 21]
35.2 = 3P - 3
35.2 + 3 = 3P
38.2 = 3P
P = 38.2/3
P ≈ 12.73
Since we are dealing with ages, we should round down P to the nearest whole number:
P = 12
So, Sam is currently 8.8 years old.
3(s-2) = 2(p-2)
4(s+3) = 3(p+3)
s = 12, p=17
two years ago, 10 = 2/3 (15) ✔
in three years, 15 = 3/4 (20) ✔
But in 20 years, 32+37 = 69