Question 1123826
Ten years ago, the sum of the ages of a mother and her daughter was seventy years. This year the mother is twice as old as her daughter. What will be the age of the daughter in ten years time?
<pre>If 10 years ago, their ages summed to 70, then today, their ages sum to 70 + 2(10) = 90
Therefore, let the daughter's age be D
Then mother's is 90 - D
We then get: 90 - D = 2D
90 = 3D
D, or daughter is {{{matrix(1,4, 90/3, "=", 30, years-old)}}}
In 10 years' time, daughter will be: {{{highlight_green(matrix(1,4, 30 + 10, "=", 40, years-old))}}}

OR

If their ages summed to 70, 10 years ago, then in ten years' time, their ages will sum to 70 + 2(20), = 110 years
Let daughter's age, 10 years from now, be D
Then mother's then, would be 110 - D
We then see that today, daughter will be D - 10, and mother will be 110 - D - 10, or 100 - D
We then get: 100 - D = 2(D - 10)
100 - D = 2D - 20
- D - 2D = - 20 - 100
- 3D = - 120
D, or daughter, in 10 years, will be: {{{highlight_green(matrix(1,4, (- 120)/(- 3), "=", 40, years-old))}}}