1.Nancy is 3 times as old as Cathy. In seven years, she will be ten years older than Cathy. What are their present age?
N = Present Nancy ages
C = Present Cathy ages
Nancy is 3 times as old as Cathy mean:
N = 3 C
In seven years Nancy will be N + 7 yrs old , Cathy will be C + 7 yrs old
In seven years, she will be ten years older than Cathy Mean:
N + 7 = C + 7 + 10
N + 7 = C + 17 Subtract 7 to both sides
N + 7 - 7 = C + 17 - 7
N = C + 10
Replace N = 3 C in this equation
3 C = C + 10 Subtract C to both sides
3 C - C = C + 10 - C
2 C = 10 Divide both sides by 2
C = 5 yrs
N = 3 C = 3 * 5 = 15 yrs
Proof:
In seven years, Nancy will 15 + 7 = 22 yrs old
Cathy will be 5 + 7 = 12 yrs old
22 - 12 = 10 yrs
To solve this problem, let's start by assigning variables to the unknowns. Let's say Nancy's age is represented by 'N' and Cathy's age is represented by 'C'.
We are given two pieces of information:
1) Nancy is 3 times as old as Cathy: This can be written as N = 3C.
2) In seven years, Nancy will be ten years older than Cathy: This can be written as N + 7 = C + 7 + 10.
Now, we can solve the system of equations to find the ages of Nancy and Cathy.
Substituting the value of N from the first equation into the second equation, we get:
3C + 7 = C + 17.
Simplifying the equation, we have:
2C = 10.
Dividing both sides by 2, we find that C = 5.
Now, substituting the value of C into the first equation, we find that N = 3 * 5 = 15.
Therefore, Nancy is 15 years old and Cathy is 5 years old.