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
x^2 + 19x + 88 = 208
x^2 + 19x - 120 = 0
(x+24)(x-5) = 0
In 5 years they will be 13 and 16
check: 13*16 = 208
This questioo
(11+x)x+11)=208
To find out how many years it will take for the product of their ages to be 208, let's first calculate their current product.
The ages of the two children are 11 and 8 years. To find the product of their ages, simply multiply them together:
11 years × 8 years = 88
So, currently, the product of their ages is 88.
Now, let's assume that after a certain number of years, the product of their ages will be 208. Let's call this number of years "x".
After x years, the age of the first child will be 11 + x years, and the age of the second child will be 8 + x years.
To find the product of their ages after x years, multiply their ages together:
(11 + x) × (8 + x) = 208
Now, we have an equation that we need to solve for x.
Expanding the equation:
88 + 19x + x^2 = 208
Rearranging the equation to bring it to a quadratic form:
x^2 + 19x + 88 - 208 = 0
x^2 + 19x - 120 = 0
To solve this quadratic equation, we can factor it, complete the square, or use the quadratic formula. Since this equation can be factored easily, let's factor it:
(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 looking for the number of years in the future, we discard the negative solution, leaving us with:
x = 8
Therefore, it will take 8 years for the product of their ages to be 208.