### Video Transcript

The ratio of Dalia’s, Amira’s, and Mariam’s ages is eight to six to seven. There is a 10-year age difference between Dalia and Amira. How old is Mariam?

The three-part ratio that we’ve been given will be in the same order as the names are listed. Dalia’s age is eight parts of this ratio, Amira’s is six, and Mariam’s is seven. We’re told that there’s a 10-year age difference between Dalia and Amira.

To answer this question, we’ll use the concept of the value of the parts in the ratio. Dalia’s age is eight parts of this ratio and Amira’s is six, which means the difference between them is two parts. Therefore, these two parts represent the 10-year age difference between Dalia and Amira.

All of the parts in a ratio are of equal size. So to find the value of one part, we can divide both sides by two. One part is equal to five years. Mariam’s age is represented by seven parts of the ratio. So to work out how old she is, we need to find the value of seven parts. To do this, we can multiply one part by seven. If one part is equal to five years, then seven parts is equal to 35 years. Mariam is 35.