The ages of two children are 11 and 8 years. In how many years' time will the product of their ages be 208?
(11+x)(8+x)=208 by expanding you get 11(8+x)+x(8+x)=208 by simplifyig this you get x^2+19x+88=208 bring 88 to the rhs you have x^2+19x=120 factorise you have x=5 or x=-24 since age cant be negative the answer is 5
(11+x) (8+x)=208. X^2+19x-120=0. Factorise so x=5 or x=-24. So the value that satisfies is 5.so it is after 5 years
the sum of the age of two sisters is 19 .in 5 years time the product of their ages will be 208.what are their age
Notebook pen . Yes
To find out in how many years' time the product of their ages will be 208, we need to determine the ages of the two children at present. We have been given that the ages of the two children are currently 11 and 8 years old.
Let's assume that after x years, the ages of the two children will be (11+x) and (8+x) respectively.
Since the product of their ages is 208, we can write the equation as:
(11+x)(8+x) = 208
To solve this equation, we can expand the equation:
88 + 11x + 8x + x^2 = 208
Combining like terms:
x^2 + 19x + 88 = 208
Rearranging the equation by subtracting 208 from both sides:
x^2 + 19x - 120 = 0
Now, we need to solve this quadratic equation for x. We can do this by factoring or using the quadratic formula:
Here, we can factor the quadratic equation:
(x+15)(x-8) = 0
Setting each factor equal to zero:
x + 15 = 0 OR x - 8 = 0
Solving for x:
x = -15 OR x = 8
Since we are interested in a positive number of years, we can ignore the negative solution. Therefore, x = 8.
Hence, in 8 years' time, the product of their ages will be 208.