A. A woman was 30 years old when her daughter was born.Her age is now 6 years more than three times her daughter's age. How old will the daughter be in 5 years?
B. Lisa is 15 years old and her father is 40. How many years ago was the father six times as old as Lisa?
C. 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?
D. 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?
A. To solve this problem, we need to set up equations based on the given information. Let's assume that the daughter's age is represented by x.
From the first sentence, we can conclude that the woman's age when her daughter was born was 30. So, the equation becomes:
Woman's age = Daughter's age + 30
From the second sentence, we know that the woman's age is now 6 years more than three times her daughter's age:
Woman's age = 3 * Daughter's age + 6
Now we can set up the equation as follows:
Daughter's age + 30 = 3 * Daughter's age + 6
Simplifying the equation:
30 - 6 = 3 * Daughter's age - Daughter's age
24 = 2 * Daughter's age
Daughter's age = 12
To find how old the daughter will be in 5 years, we add 5 to her current age:
Daughter's age in 5 years = 12 + 5 = 17
Therefore, the daughter will be 17 years old in 5 years.
B. Let's set up equations based on the given information. Let's assume the number of years ago is represented by x.
From the second sentence, we can determine that Lisa's current age is 15, and her father's age is 40.
To find how many years ago the father was six times as old as Lisa, we can set up the equation:
Father's age - x = 6 * (Lisa's age - x)
Substituting the values we have:
40 - x = 6 * (15 - x)
Now we can solve for x:
40 - x = 90 - 6x
5x = 50
x = 10
Therefore, the father was six times as old as Lisa 10 years ago.
C. To solve this problem, let's set up equations based on the given information. Let Joel's age be represented by x and Bob's age be represented by y.
From the first sentence, we can conclude that Joel is one third the age of Bob:
x = (1/3)y
From the second sentence, we know that in 7 years, the combined ages of the boys will be 58:
(x + 7) + (y + 7) = 58
Now we can solve these equations together. We will substitute the first equation into the second equation:
[(1/3)y + 7) + (y + 7) = 58
Simplifying the equation:
(1/3)y + 7 + y + 7 = 58
(4/3)y + 14 = 58
(4/3)y = 58 - 14
(4/3)y = 44
4y = 132
y = 33
Now that we know Bob's age (y), we can substitute it into the first equation to find Joel's age (x):
x = (1/3)(33)
x = 11
Therefore, Joel is 11 years old and Bob is 33 years old.
D. Let's set up equations based on the given information. Let Tom's age be represented by x and Leigh Ann's age be represented by y.
From the first sentence, we can conclude that Tom is three times as old as Leigh Ann:
x = 3y
From the second sentence, we know that 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:
(x + 7) = (1/2)x + (1/3)(y + 7)
Now we can solve these equations together. We will substitute the first equation into the second equation:
(3y + 7) = (1/2)(3y) + (1/3)(y + 7)
Simplifying the equation:
3y + 7 = (3/2)y + (1/3)y + 7/3
3y - (3/2)y - (1/3)y = -7/3 + 7
(5/6)y = (7 - 7/3)
(5/6)y = (21/3 - 7/3)
(5/6)y = 14/3
y = (14/3) * (6/5)
y = 8
Now that we know Leigh Ann's age (y), we can substitute it into the first equation to find Tom's age (x):
x = 3 * 8
x = 24
Therefore, Tom is currently 24 years old.
To find Tom's age in 7 years, we add 7 to his current age:
Tom's age in 7 years = 24 + 7 = 31
Therefore, Tom will be 31 years old in 7 years.
A.
n years ago, daughter was born. So now mother is n+30 and daughter is n
n+30 = 3n+6
n = 12
In 5 years daughter will be 17
B.
n years ago
6(15-n) = 40-n
n = 10
C.
3j=b
j+7+b+7=58
4j=44
j=11
b=33
D.
t=3a
t/2 + (a+7)/3 = t
3a/2 + (a+7)/3 = 3a
9a + 2a+14 = 18a
a = 2
t+7 = 13