SOLUTION: how do i work out a word problem in algebra format. john is 4 years younger than his sister mary. the sum of their ages is 20. using algebra by letting marys age = x and constructi

Just rewrite those two sentences using the words 

1. John's age
2. Mary's age
3. equals
4. minus
5. plus

"John is 4 years younger than his sister Mary"

can be rewritten as

"John's age equals Mary's age minus 4 years"

then you can put in = and - and get:

John's age = Mary's age - 4

Now rewrite:

"The sum of their ages is 20" using the above 5 words:

as

"John's age plus Mary's age equals 20"

then you can put in + and = and get:

John's age + Mary's age = 20.

Now let's look at the two sentences:


John's age = Mary's age - 4
John's age + Mary's age = 20.

Now let Mary's age = M, then we have:

John's age = M - 4
John's age + M = 20.

Now let's rewrite the second sentence but instead of 
"John's age" let's substitute M - 4 since the first sentence
tells us that's what John's age equals to:


John's age + M = 20

becomes

M - 4 + M = 20

Now collect the two like terms M and M and get 2M

2M - 4 = 20

Now add 4 to both sides and get

    2M = 24

Now divide both sides by 2 and get

     M = 12

So Mary's age is 12.

Now since 

John's age = M - 4

John's age = 12 - 4

John's age = 8

So Mary is 12 and John is 8.

Check: Mary is 4 years older than John because 12 is 4 more than 8

The sum of their ages is 20 because the sum of 12 and 8 is 20.

So it's correct.  Study the above carefully and maybe you'll
start to see how to translate English into algebra. 

Edwin