Jen is 26 years younger than her mom. Together, their ages total 50. How old is Jen? How old is her Mom?

My 4th grader has not learned algebra yet, so how do we solve this?

if you are against using any algebra, just start trying numbers that add to 50. You want two which are 26 apart.

10+40=50, but they are 30 apart.

Each number you add to 10 and subtract from 40 reduces the distance by 2.

So, 12+38 = 50

To solve this problem without algebra, we can use a method called "guess and check" or "trial and error." We will start by making a guess and checking if it satisfies the given conditions. If our guess is incorrect, we will adjust our guess until we find the correct answer.

Let's start by guessing Jen's age. Since we know that Jen is 26 years younger than her mom, we can choose an age for Jen and determine her mom's age.

Let's say we guess that Jen is 10 years old. If Jen is 10 years old, then her mom would be 10 + 26 = 36 years old. We need to check if the sum of their ages is 50.

The sum of their ages (10 + 36) is 46, which is less than 50. Since our guess resulted in a sum that is too small, we need to increase our guess for Jen's age.

Let's try again and guess that Jen is 15 years old. If Jen is 15 years old, then her mom would be 15 + 26 = 41 years old. We check if the sum of their ages is 50.

The sum of their ages (15 + 41) is 56, which is greater than 50. Since our guess resulted in a sum that is too large, we need to decrease our guess for Jen's age.

Let's try again and guess that Jen is 13 years old. If Jen is 13 years old, then her mom would be 13 + 26 = 39 years old. We check if the sum of their ages is 50.

The sum of their ages (13 + 39) is 52, which is greater than 50. We are getting closer, but it is still too large.

Let's keep adjusting our guess until we find the correct answer.

If we guess that Jen is 12 years old, then her mom would be 12 + 26 = 38 years old. We check if the sum of their ages is 50.

The sum of their ages (12 + 38) is 50, which is the correct answer!

Therefore, Jen is 12 years old, and her mom is 38 years old.