Thread: Setting up linear equations.

In a practise GCSE mock exam paper i saw these 3 questions and i think i have got the right answers but i wondered if you could just check for me.

1. A girl is Y years old. Her father is 23 years older than she is. The sum of their ages is 37. How old is the girl?
So i did this:
Y + 23 = 37
37 - 23 = 14

2. A boy is X years old. His sister is twice as old as he is. The sum of their ages is 24. How old is the boy?
So i did this:
X times X = 24
24 divided by 2 = 12

3. On a bookshelf there are 2b crime novels, 3b - 2 science fiction novels and b + 7 romance novels. Find how many of each type of book there is, if there are 65 books altogether.
So i did this:
2b + 3b - 2 + b + 7 = 65
then i simplified it: 6b - 9 = 65
i then added 9 to both of the whole numbers so i now have:
6b = 74
And then i divided each side by 6.
So i now have b = 12.5
so.. Crime novels = 2 x 23.5 = 25
Science fiction novels: 3 x 12.5 = 37.5 and then i - 2 which equals 35.5
Romance novels: 12.5 + 7 = 19.5

Please can you tell me if i've gone wrong in any of these problems.
Thanks in advance

Originally Posted by mollyx

In a practise GCSE mock exam paper i saw these 3 questions and i think i have got the right answers but i wondered if you could just check for me.

1. A girl is Y years old. Her father is 23 years older than she is. The sum of their ages is 37. How old is the girl?
So i did this:
Y + 23 = 37 Not quite. The father's age is Y + 23. But the sum of their ages is 37. That means the girl's age (Y) added to the father's (Y+23) is 37, so Y+Y+23=37
37 - 23 = 14

2. A boy is X years old. His sister is twice as old as he is. The sum of their ages is 24. How old is the boy?
So i did this:
X times X = 24 Not quite. If his sister is twice as old as he is, then she is '2x' years old. If their ages added together are 24, then 2x+x=24. Try again from here.
24 divided by 2 = 12

3. On a bookshelf there are 2b crime novels, 3b - 2 science fiction novels and b + 7 romance novels. Find how many of each type of book there is, if there are 65 books altogether.
So i did this:
2b + 3b - 2 + b + 7 = 65
then i simplified it: 6b - 9 = 65 Check this stage. You've made a sign error.
i then added 9 to both of the whole numbers so i now have:
6b = 74
And then i divided each side by 6.
So i now have b = 12.5
so.. Crime novels = 2 x 23.5 = 25
Science fiction novels: 3 x 12.5 = 37.5 and then i - 2 which equals 35.5
Romance novels: 12.5 + 7 = 19.5

Please can you tell me if i've gone wrong in any of these problems.
Thanks in advance

Corrections shown.

I don't get how i've made mistakes?

Originally Posted by mollyx

I don't get how i've made mistakes?

You have just made a slight muddle with the question. In the first question, The girl is aged Y. The father is 23 years older. So he is Y+23.
Age of girl: Y
Age of Father:Y+23
Age of Girl + Age of Father: Y+Y+23 (=37)

For b, You know the person is aged X. His sister is twice as old as he is, so she is 2X
Age of boy: X
Age of sister:2X
Sum of their ages: X+2X (=24)

For C, you've almost got it! You've made a slight sign error where I indicated. It should be 6b+5=65, can you see why?

Yeah i can see why now!
Thank you!