A. 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?
B. 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?
C. 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?
thank you
john's present age is at least three times as great as his age 10 years ago. Find the greatest possible age of john at present
A.
J=10 + M
3J +5=5M-5
3(10+M)+5=5M-5
30+3M+5=5M-5
2M=40
M=20
J=10+M=30
J=10+m
3J+5=5m–5
3(10+m)=5m–10
30+3m=5m–10
2m=40
M=20
And J=10+m
10+30
J=40
A. Let's solve this problem step by step.
Let's assume Marcus is M years old now. According to the given information, John is 10 years older than Marcus. So, John's age would be M + 10 years.
Five years from now, John's age would be (M + 10) + 5 = M + 15 years.
According to the problem, three times John's age 5 years from now will be the same as five times Marcus's age 5 years ago. So we can write the equation:
3(M + 15) = 5(M - 5)
Now we can solve for M, which is Marcus's age.
Expanding the equation:
3M + 45 = 5M - 25
Rearranging the equation:
5M - 3M = 45 + 25
2M = 70
Dividing both sides of the equation by 2:
M = 35
Therefore, Marcus is currently 35 years old.
To find John's age, we substitute the value of M into the expression we derived for John's age earlier:
John's age = M + 10 = 35 + 10 = 45 years.
So, John is 45 years old now.
B. Let's solve this problem step by step as well.
Let's assume Danielle's age now is D. 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 4D.
Ten years from then, Danielle's age will be D + 10 and Kristen's age will be 4D + 10.
According to the problem, ten years from then, Kristen will only be twice as old as Danielle. So we can write the equation:
4D + 10 = 2(D + 10)
Now we can solve for D, which is Danielle's age.
Expanding the equation:
4D + 10 = 2D + 20
Rearranging the equation:
4D - 2D = 20 - 10
2D = 10
Dividing both sides of the equation by 2:
D = 5
Therefore, Danielle's current age is 5 years.
To find Kristen's age, we substitute the value of D into the expression we derived for Kristen's age earlier:
Kristen's age = 4D = 4 * 5 = 20 years.
So, Kristen is currently 20 years old.
C. Let's solve this problem step by step.
Let's assume the daughter's age now is D. According to the given information, the woman was 30 years old when her daughter was born. So the woman's age would be D + 30 years.
According to the problem, the woman's age is now 6 years more than three times her daughter's age. So we can write the equation:
D + 30 = 3D + 6
Now we can solve for D, which is the daughter's age.
Rearranging the equation:
3D - D = 30 - 6
2D = 24
Dividing both sides of the equation by 2:
D = 12
Therefore, the daughter's current age is 12 years.
To find the daughter's age in 5 years, we add 5 to her current age:
Daughter's age in 5 years = 12 + 5 = 17 years.
So, the daughter will be 17 years old in 5 years.
1. John is now 45 years old.
45 (John) ---- 50 X 3 = 150
35 (Marcus) ---- 30 X 5 = 150