1. Lisa is 15 years old and her father is 40. How many years ago was the father six times as old as Lisa?
2. Joel is one third the age of Bob. In 7 years the combined ages of the boys will be 58. How old is each boy now?
3. Tom is three times as old as Leigh Ann. In 7 years, the sum of half of Tom's present age and a third of Leigh Ann's age will be the same as Tom's age now. How old will Tom be in 7 years?
Let it be x yrs ago, when Lisa was 15-x and her father was 40-x. Then-
40-x=6(15-x) or 40-x=90-6x
Or 6x-x=90-40 or 5x=50 thus x=5.
Let Bob be x yrs and Joel be 3x. Then (x+7)+(3x+7)=58 or 4x+14=85
Or 4x=44 hence x=11. Thus Bob is 11 and Joel is 33. After 7 yrs Bob willbe 18 and Joel will be 40. 18+40=58 OK.
Let Leigh be x and Tom be 3x at present. After 7 yrs, Leigh will be x+7 and Tom will be 3x+7. Then,
(x+7)/2 + (3x+7)/3=3x
Or 2x+14+9x+21=3x
Or, 7x=21+14=35 or x=5. Tom is 15.
Check: After 7 yrs Leigh will be 12 and Tom will be 22.
12/3 + 22/2=4+11=15. OK.
6(15-x) = 40-x
Thus : x = 10
Question 1, X is supposed to be 10
To solve these questions, we can use algebraic expressions and equations. Let's break down each question step by step to understand how to find the solutions.
1. Lisa is 15 years old and her father is 40. How many years ago was the father six times as old as Lisa?
Let's assume that "x" represents the number of years ago when the father was six times as old as Lisa. To solve this question, we can set up an equation based on the given information.
Father's current age = 40
Lisa's current age = 15
Father's age "x" years ago = 40 - x
Lisa's age "x" years ago = 15 - x
According to the question, the father's age "x" years ago was six times Lisa's age "x" years ago. Therefore, we can set up the equation:
40 - x = 6(15 - x)
Now, let's solve the equation:
40 - x = 90 - 6x
5x = 50
x = 10
Therefore, ten years ago, the father was six times as old as Lisa.
2. Joel is one third the age of Bob. In 7 years, the combined ages of the boys will be 58. How old is each boy now?
Let's assume that "x" represents Bob's current age. Based on the given information, Joel's age would be one-third of Bob's age, which can be represented as (1/3)x.
According to the second condition, the combined ages of the boys in 7 years will be 58. Therefore, we can set up the equation:
(x + 7) + ((1/3)x + 7) = 58
Let's solve the equation:
(x + 7) + (x/3 + 7) = 58
Multiply the equation by 3 to remove the fraction:
3(x + 7) + x + 7 = 174
4x + 28 = 174
4x = 146
x = 36.5
Bob's current age (x) is 36.5 years old.
Joel's age is one-third of Bob's age, so Joel's current age is (1/3) * 36.5 = 12.17 (approximately 12 years old).
Therefore, Bob is 36.5 years old, and Joel is approximately 12 years old.
3. Tom is three times as old as Leigh Ann. In 7 years, the sum of half of Tom's present age and a third of Leigh Ann's age will be the same as Tom's age now. How old will Tom be in 7 years?
Let's assume that "x" represents Leigh Ann's current age. Based on the given information, Tom's age would be three times Leigh Ann's age, which can be represented as 3x.
According to the second condition, the sum of half of Tom's current age and a third of Leigh Ann's age in 7 years will be equal to Tom's current age. Therefore, we can set up the equation:
(3x/2 + 7) + (x/3 + 7) = 3x
Let's solve the equation:
(3x/2 + 7) + (x/3 + 7) = 3x
Multiply the equation by 6 to remove the fractions:
9x + 42 + 2x + 42 = 18x
11x + 84 = 18x
7x = 84
x = 12
Therefore, Leigh Ann's current age (x) is 12 years old. Tom's current age is three times Leigh Ann's age, so Tom's current age is 3 * 12 = 36 years old.
In 7 years, Tom will be 36 + 7 = 43 years old.