The ages of two sisters are 11 and 8 years. In how many years time will the product of their ages be 208?
Let the number of years be $x$. Then, in $x$ years, the ages of the two sisters will be $11+x$ and $8+x$. We have the equation $(11+x)(8+x)=208$, which expands to $x^2+19x-40=0$. Factoring, we get $(x+20)(x-1)=0$, so either $x=-20$ or $x=1$. Since time cannot be negative, the answer is $\boxed{1}$ year.
To find in how many years time the product of the ages of two sisters will be 208, we can set up an equation.
Let's say x represents the number of years.
After x years, the age of the first sister will be 11 + x, and the age of the second sister will be 8 + x.
The equation for the product of their ages after x years is:
(11 + x)(8 + x) = 208
Now, let's solve this equation step by step:
Step 1: Expand the equation
(11 + x)(8 + x) = 208
88 + 11x + 8x + x^2 = 208
Step 2: Simplify the equation
x^2 + 19x + 88 = 208
Step 3: Move all terms to one side of the equation
x^2 + 19x + 88 - 208 = 0
Step 4: Combine like terms
x^2 + 19x - 120 = 0
Step 5: Factor the quadratic equation
(x + 15)(x - 8) = 0
Step 6: Set each factor equal to zero and solve for x
x + 15 = 0 or x - 8 = 0
If x + 15 = 0, then x = -15, but negative ages don't make sense in this context, so we can discard this solution.
If x - 8 = 0, then x = 8.
Therefore, in 8 years' time, the product of their ages will be 208.
To solve this problem, we need to find out in how many years the product of the two sisters' ages will be 208. Let's break it down step by step.
Let's assume that "x" represents the number of years from now. So, the older sister's age after "x" years will be 11 + x, and the younger sister's age after "x" years will be 8 + x.
The problem states that the product of their ages after "x" years will be 208. Mathematically, this can be represented as:
(11 + x) * (8 + x) = 208
To solve this equation, we can expand it:
88 + 19x + x^2 = 208
Rearranging the equation to make it equal to zero:
x^2 + 19x + 88 - 208 = 0
Simplifying the equation:
x^2 + 19x - 120 = 0
To solve this quadratic equation, we can factor or use the quadratic formula.
Factoring:
(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 it doesn't make sense to have a negative number of years, we disregard the solution x = -15.
Therefore, the number of years from now when the product of their ages will be 208 is 8 years.