SOLUTION: Lester is older than John by 7 years. 15 years back John's age was 3/4 of Lester's age. Find their present ages.

Question 1143571: Lester is older than John by 7 years. 15 years back John's age was 3/4 of Lester's age. Find their present ages.
Found 3 solutions by mathmadeeasy, MathTherapy, ikleyn:
Answer by mathmadeeasy(2)   (Show Source): You can put this solution on YOUR website!
Let L = Lester's present age
J = John's present age
Given:
1. Lester is older than John by 7 years: L = J + 7
2. 15 years back John's age was 3/4 of Lester's (present) age: J - 15 = 3/4 L
Solution:
I. L = J + 7
J - 15 = 3/4L
L = J + 7
J = 3/4L + 15
II. L = 3/4L + 15 + 7
L = 3/4L + 22
L - 3/4L = 22
4/4L - 3/4L = 22
1/4L = 22
4*(1/4)L = 22*4
L = 88
Testing the given:
1. L = J + 7
88 = J + 7
88 - 7 = J
J = 81
2. J - 15 = 3/4L
81 - 15 = 3/4(88)
66 = 66
Fifteen years back, John's age (was 66) was 3/4 off Lester's (present) age of 88.

Answer:
Lester's present age is 88 while John's present age is 81.

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Lester is older than John by 7 years. 15 years back John's age was 3/4 of Lester's age. Find their present ages.

It's more likely that this should've read: ".........15 years back John's age was 3/4 of Lester's age," then/at that time!
Having said that, that person's answers are INCORRECT.
Correct answers:
Answer by ikleyn(52812)   (Show Source): You can put this solution on YOUR website!
.

Let L be the Lester's age; then the John's age is L-7 years. 15 years back John's age was ((L-7)-15) = L-21; Lester's age was L-15 years. The condition says L - 22 = . Solve this equation step by step. Start multiplying both sides by 4. 4L - 88 = 3*(L-15) 4L - 88 = 3L - 45 4l - 3L = 88 - 45 L = 43. ANSWER. Lester is 43 years old; John is 43 - 7 = 36 years old. CHECK. 43 - 15 = 28; 36 - 15 = 21; 21 = . ! Correct !

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There is a bunch of lessons on age word problems
    - Age problems and their solutions
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    - Really intricate age word problem
    - Selected age word problems from the archive
    - Age problems for mental solution
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The referred lessons are the part of this online textbook under the topic "Age word problems".

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