5 years ago, Peeta was twice as old as his daughter, Katniss. In ten years, the sum of their ages will equal 90. Find their current ages.

Answer 1

Let's start by assigning variables to their current ages.

Let 'P' represent Peeta's current age and 'K' represent Katniss's current age.

According to the information given, 5 years ago, Peeta was twice as old as Katniss, so we can create the equation:

(P - 5) = 2(K - 5)

In ten years, the sum of their ages will equal 90, so we can create the equation:

(P + 10) + (K + 10) = 90

Now, we have a system of equations:

(P - 5) = 2(K - 5)
(P + 10) + (K + 10) = 90

First, let's solve the first equation for P in terms of K.

Expand:
P - 5 = 2K - 10
P = 2K - 5

Now, substitute this expression for P in the second equation:

(2K - 5 + 10) + (K + 10) = 90
2K + K + 15 + 10 = 90
3K + 25 = 90

Subtract 25 from both sides:
3K = 65

Divide both sides by 3:
K = 65 / 3 = 21.6667

Katniss's current age, when rounded to the nearest whole number, is 22.

Now, substitute this value back into the first equation to solve for P:

P = 2K - 5
P = 2(22) - 5
P = 44 - 5
P = 39

Therefore, Peeta's current age is 39 and Katniss's current age is 22.

Answer 2

No.

Answer 3

Apologies for the incorrect solution.

Let's start by assigning variables to their current ages: Let P represent Peeta's current age and K represent Katniss's current age.

According to the information given, 5 years ago Peeta was twice as old as Katniss. So, we can create the equation: P - 5 = 2(K - 5).

In ten years, the sum of their ages will equal 90. So, we can create the equation: (P + 10) + (K + 10) = 90.

Now, we have a system of equations:
P - 5 = 2(K - 5)
(P + 10) + (K + 10) = 90.

Let's solve this system of equations:

From the first equation, we can simplify: P - 5 = 2K - 10.
By rearranging terms, we have P - 2K = -5.

Next, we'll rewrite the second equation: P + K + 20 = 90.

Now we have a system of equations:
P - 2K = -5
P + K = 70.

To solve this system, you can use substitution or elimination method. We'll use the elimination method here.

Multiply the second equation by 2 to eliminate the P term: 2(P + K) = 2(70) -> 2P + 2K = 140.

Now, we can sum the two equations: (P - 2K) + (2P + 2K) = -5 + 140.
This simplifies to 3P = 135.
Divide both sides by 3: P = 45.

Substitute the value of P back into the second equation:
45 + K = 70.
Subtract 45 from both sides: K = 25.

Therefore, Peeta's current age is 45 and Katniss's current age is 25.