the ages of two brothers are 11 and 8 years.
In how many years time will the product of their ages be 208?
(11+x)(8+x) = 208
Solve for x.
Let's solve this problem step-by-step:
Step 1: Determine the current ages of the brothers.
According to the information given, one brother is 11 years old, and the other brother is 8 years old.
Step 2: Find the product of their ages.
The product of their ages can be calculated by multiplying the two ages together:
11 × 8 = 88
Step 3: Determine the difference needed for the product to be 208.
To find the difference needed for the product of their ages to be 208, subtract the current product from 208:
208 - 88 = 120
Step 4: Calculate the number of years needed for the product to be 208.
In how many years will their product be 208? Let's assume this number of years is represented by 'x'. The equation to solve is:
(11 + x) × (8 + x) = 208
Step 5: Solve the equation.
Expand the equation:
88 + 8x + 11x + x^2 = 208
Rearrange the equation:
x^2 + 19x + 88 = 208
Subtract 208 from both sides:
x^2 + 19x + 88 - 208 = 0
x^2 + 19x - 120 = 0
Factorize the equation:
(x + 15)(x - 8) = 0
Solve for x:
x + 15 = 0 or x - 8 = 0
x = -15 or x = 8
Since the number of years cannot be negative, we disregard -15 as a solution.
Therefore, in 8 years' time, the product of their ages will be 208.
To find out in how many years the product of their ages will be 208, we need to set up an equation.
Let x represent the number of years elapsed. The age of the older brother in x years would be 11 + x, and the age of the younger brother in x years would be 8 + x.
The product of their ages in x years would be (11 + x) * (8 + x). We want this product to be equal to 208:
(11 + x) * (8 + x) = 208
To solve this equation, we can either expand and simplify it, or use a graphing calculator. Let's expand and simplify it:
(11 + x) * (8 + x) = 208
88 + 11x + 8x + x^2 = 208
x^2 + 19x + 88 = 208
Now, let's subtract 208 from both sides:
x^2 + 19x + 88 - 208 = 0
x^2 + 19x - 120 = 0
We now have a quadratic equation. To solve it, we can either factor it or use the quadratic formula. In this case, the equation can be factored:
(x + 15)(x - 8) = 0
Setting each factor to zero, we get:
x + 15 = 0 or x - 8 = 0
Solving each equation separately:
x = -15 or x = 8
Since we are talking about the number of years elapsed, a negative value doesn't make sense in this context. Therefore, the answer is x = 8 years.
In 8 years, the product of their ages will be 208.