the sum of Emmas age and her sister's age is 41. Emma is 11 years older than her sister. What is Emmas age, and what is her sisters age?

Question

Solve by using substitution method

Answer 1

Octavia, the hard part about word problems is usually translation from English into Math.

 

The first thing to do is to identify the quantities involved.

Let e be Emma‘s age.

Let s be sister’s age.

 

Next, Translate the words into equations.

Translate “sum” into “addition”. Specifically, Translate 

“the sum of Emmas age and her sister's age is 41” into

“e + s = 41”

Next, Translate “Emma is 11 years older than her sister” into

“e = 11 + s”

 

Now you have two equations. you can substitute “11 + s” for “e” in the first equation.

e + s = 41

substitute 11 + s for e

(11+s) + s = 41

 

at this point, you have one equation, so collect like terms, and solve for s (sister‘s age). Then substitute that value into “e + s = 41”, and solve for e (Emma’s age).

 

Let me know if you need more help!