A. Brad is 12 years older than Sam . If Brad were 8 years older than he is now. he would be twice as old as Sam. How old is Sam now?
B. Barrie is now 2 years older than Krista. In 15 years Barrie's age will be 2 years more than twice Krista's age now. How old will Barrie be in 6 years?
C. John is now 10 years older than Marcus. Three times John's age 5 years from now will be the same as five times Marcus's age 5 years ago. How old is John now?
D. In 1 year Kristen will be four times as old as Danielle. Ten years from then Kristen will only be twice as old as Danielle. How old is Kristen now?
A. 12+x+8=2x
20+x=2x
(subtract "x" from both sides)
x=20
B. x+2+15=2+2x
(subtract "2" from both sides)
x+15=2x
(subtract "x" from both sides)
x=15 (Krista's age)
15+2=17 (Barrie's age now)
17+6=23
Phil is three times as old as Carrie. Five years ago, phil was four times as old as Carrie was at that time. How old is Carrie now?
A. Let's represent Sam's age as "S" and Brad's age as "B".
According to the given information, Brad is 12 years older than Sam: B = S + 12
If Brad were 8 years older than he is now, his age would be B + 8.
According to the second piece of information given, Brad's age would be twice as old as Sam's age:
B + 8 = 2S
Now we can solve these equations simultaneously to find the value of S (Sam's age):
B = S + 12
B + 8 = 2S
Substituting the first equation into the second equation:
S + 12 + 8 = 2S
S + 20 = 2S
20 = S
Therefore, Sam is 20 years old.
B. Let's represent Krista's age as "K" and Barrie's age as "B".
According to the given information, Barrie is 2 years older than Krista: B = K + 2
In 15 years, Barrie's age will be B + 15 and Krista's age now is K.
According to the second piece of information given, Barrie's age in 15 years will be 2 more than twice Krista's age now:
B + 15 = 2K + 2
To find out how old Barrie will be in 6 years, we can use the first equation:
B + 6 = K + 2 + 6
B + 6 = K + 8
So, Barrie will be the same age as Krista in 6 years, which is K + 8.
C. Let's represent John's age now as "J" and Marcus's age now as "M".
According to the given information, John is now 10 years older than Marcus: J = M + 10
Three times John's age 5 years from now will be 3(J + 5), and five times Marcus's age 5 years ago will be 5(M - 5).
According to the second piece of information given, these two values are equal:
3(J + 5) = 5(M - 5)
To find out John's age now, we solve this equation. However, there isn't enough information to solve it uniquely. More information is needed to find John's age.
D. Let's represent Kristen's age as "K" and Danielle's age as "D".
According to the given information, in 1 year Kristen will be four times as old as Danielle: K + 1 = 4(D + 1)
Ten years from then, Kristen will only be twice as old as Danielle: K + 1 + 10 = 2(D + 1 + 10)
Let's simplify these equations to solve for Kristen's age now:
K + 1 = 4D + 4
K + 11 = 2D + 22
Subtracting the first equation from the second equation:
(K + 11) - (K + 1) = (2D + 22) - (4D + 4)
10 = 2D + 18
2D = -8
D = -4
Since it doesn't make sense for Danielle to have a negative age, there is likely an error in the given information or another piece of information is needed to solve the problem.
A. To figure out the age of Sam, let's start by assigning a variable to Sam's age. Let's say Sam's age is represented by "x" years.
According to the given information, Brad is 12 years older than Sam, so his age would be (x + 12) years.
Next, the problem states that if Brad were 8 years older than he is now, he would be twice as old as Sam. This can be written as the equation:
(x + 12) + 8 = 2x
Now, we can solve this equation to find the value of x, which represents Sam's current age:
x + 20 = 2x
Subtracting "x" from both sides, we get:
20 = x
Therefore, Sam is currently 20 years old.
B. Let's assign a variable to Krista's age. Let's say Krista's age is represented by "x" years.
According to the given information, Barrie is now 2 years older than Krista, so Barrie's age would be (x + 2) years.
The problem states that in 15 years, Barrie's age will be 2 years more than twice Krista's age now. This can be written as the equation:
(x + 2) + 15 = 2x + 2
Now, we can solve this equation to find the value of x, which represents Krista's current age:
x + 17 = 2x + 2
Subtracting 2x from both sides and subtracting 17 from both sides, we get:
x - 2x = 2 - 17
-x = -15
Multiplying both sides of the equation by -1, we get:
x = 15
Therefore, Krista is currently 15 years old.
To find out how old Barrie will be in 6 years, we just add 6 to his current age:
Barrie's age in 6 years = (x + 2) + 6 = 15 + 2 + 6 = 23 years old.
C. Let's assign a variable to Marcus's age. Let's say Marcus's age is represented by "x" years.
According to the given information, John is now 10 years older than Marcus, so John's age would be (x + 10) years.
The problem states that three times John's age 5 years from now will be the same as five times Marcus's age 5 years ago. This can be written as the equation:
3[(x + 10) + 5] = 5(x - 5)
Now, we can solve this equation to find the value of x, which represents Marcus's current age:
3(x + 15) = 5(x - 5)
Expanding the equation, we get:
3x + 45 = 5x - 25
Subtracting 3x from both sides and adding 25 to both sides, we get:
45 + 25 = 5x - 3x
70 = 2x
Dividing both sides of the equation by 2, we get:
x = 35
Therefore, Marcus is currently 35 years old.
To find out John's age, we can substitute the value of x into the equation:
John's age = x + 10 = 35 + 10 = 45 years old.
D. Let's assign a variable to Danielle's age. Let's say Danielle's age is represented by "x" years.
According to the given information, in 1 year, Kristen will be four times as old as Danielle, so Kristen's age in 1 year would be 4x.
The problem also states that ten years from then, Kristen will only be twice as old as Danielle, so Kristen's age in 11 years from now would be 2(x + 11).
Setting up the equation:
4x + 1 + 10 = 2(x + 11)
Simplifying the equation, we get:
4x + 11 = 2x + 22
Subtracting 2x from both sides and subtracting 11 from both sides, we get:
4x - 2x = 22 - 11
2x = 11
Dividing both sides by 2, we get:
x = 5.5
Since ages are typically whole numbers, we can consider that Danielle's current age is also 5 years. Therefore, Kristen's current age would be 4 times that:
Kristen's age = 4x = 4 * 5 = 20 years old.
Therefore, Kristen is currently 20 years old.