# Thread: Year 11 - Worded question

1. ## Year 11 - Worded question

I've done the whole exercie of worded questions but I'm struggling with these two.

6. In four years time a mother will be three times as old as her son. Four years ago she was five times as old as her son. Find their present ages.

8. Two children had 110 marbles between them. After one child had lost half her marbles and the other had lost 20 they had an dqual number. How many marbles did each child start with and how many did they finish with?

I can do it with trial and error but it'd be much more helpful in algebraic terms as this is an algebra topic.

2. 8. Two children had 110 marbles between them. After one child had lost half her marbles and the other had lost 20 they had an dqual number. How many marbles did each child start with and how many did they finish with?
After one child had lost half her marbles and the other had lost 20 they had an equal number.

1st child=x
2nd child is=110-x

$\displaystyle x-\frac{x}{2}=110-x-20$

let's say 1/2 is 60

$\displaystyle \frac{2x-x}{2}=110-x-20$

$\displaystyle \frac{3}{2}x=90$

x=60

$\displaystyle 60-30=110-60-20$

$\displaystyle 30=30$
do we have the same answer? i'll try the other question.

3. Originally Posted by princess_21
After one child had lost half her marbles and the other had lost 20 they had an equal number.

1st child=x
2nd child is=100-x

$\displaystyle x-\frac{1}{2}=100-x-20$

let's say 1/2 is 26

$\displaystyle 53-26=100-53-20$

$\displaystyle 57=57$

do we have the same answer? i'll try the other question.
Let one Child has x marbles so the other will have 110-x marbles

So
according to question
$\displaystyle \frac{x}{2}= 110-x-20$
so $\displaystyle \frac{3x}{2} =90$
Thus

$\displaystyle x= \frac{180}{3}$
x = 60

@Princess watch "110" and the second step, otherwise you are completely right

4. 6. In four years time a mother will be three times as old as her son. Four years ago she was five times as old as her son. Find their present ages.

4yrs ago
son=x
mother=5x

present
son=x+4
mother=5x+4

+4yrs
son=x+8
mother=5x+8

equation:
$\displaystyle 5x+8=3(x+8)$

$\displaystyle 5x+8=3x+24$

$\displaystyle 5x-3x=24-8$

$\displaystyle 2x=16$

$\displaystyle x=8$

4yrs ago
son=x--$\displaystyle 8$

mother=5x---$\displaystyle 40$

present
son=x+4--- $\displaystyle 12$

mother=5x+4---$\displaystyle 44$

+4yrs
son=x+8---$\displaystyle 16$

mother=5x+8$\displaystyle 48$

in present time the son is 12 yrs old
mother is 44yrs old

do we have the same answer?

5. Originally Posted by nimrod
I've done the whole exercie of worded questions but I'm struggling with these two.

6. In four years time a mother will be three times as old as her son. Four years ago she was five times as old as her son. Find their present ages.
Let the mathers age is x
And age of son be y

so
(x+4) =3(y+4)
and
(x-4) = 5(y-4)

Get the values of x and y now and tell in case if you still have trouble
If you want to follow single variable follow Princess