Question

casey is six time as old as Ralph, In two years, she will be four time as old as Ralph. How old is each of them now?

Answer 1

To solve for the ages of Casey and Ralph, we set r to represent Ralph's current age, determined Casey's age as 6r, and used the future age relation to create the equation 6r + 2 = 4(r + 2). Solving it, Ralph is 3 years old and Casey is 18 years old.

Step-by-step explanation:

The problem stated involves determining the current age of both Casey and Ralph based on their age relationship now and in the future. To solve this, we need to create equations based on the information given and solve for the variable representing the age. Let's use r to represent Ralph's current age.

According to the problem, Casey is six times as old as Ralph, which means Casey's current age is 6r. It is also given that in two years, Casey will be four times as old as Ralph. At that time, Ralph would be r+2 years old, and Casey would be 6r+2 years old.

We can set up an equation to represent the future ages: 6r + 2 = 4(r + 2). By solving this equation, we can determine Ralph's current age and consequently Casey's current age.

Solving the equation:

• 6r + 2 = 4(r + 2)
• 6r + 2 = 4r + 8
• 6r - 4r = 8 - 2
• 2r = 6
• r = 3

Now that we've determined that Ralph's age is 3, we can calculate Casey's age: Casey is 6 × 3 = 18 years old.

So, Ralph is currently 3 years old and Casey is 18 years old.

Answer 2

Statement 1: Casey is 6 times as old as Ralph gives

C = 6R

where C and R represent Casey and Ralph’s current ages respectively.
Statement 2: In 2 years, Casey will be four times as old as Ralph gives

C + 2 = 4 (R + 2)

Expanding the brackets gives

C + 2 = 4R + 8

Substituting in C from the first equation gives

6R + 2 = 4R + 8

Which can be rearranged as

2R = 6

Implying R = 3 and C = 6R = 18

Therefore, Ralph is 3; Casey is 18