(a) Form an equation in terms of $x$.
(b) Solve the equation and work out Robert's and Hannah's ages.
Robert is x years old.
Hannah is 7 years younger than Robert. The sum of their ages is 61.
Answer (1)
Represent Robert's age as x and Hannah's age as x − 7 .
Form the equation x + ( x − 7 ) = 61 based on the sum of their ages.
Solve the equation to find x = 34 , which is Robert's age.
Calculate Hannah's age: 34 − 7 = 27 .
Robert is 34 years old and Hannah is 27 years old: R o b er t = 34 , H annah = 27
Explanation
Understanding the Problem Let's break down this problem step by step. We know Robert's age is represented by x , and Hannah is 7 years younger than Robert. We also know that the sum of their ages is 61. Our goal is to form an equation using this information and then solve for x to find their ages.
Forming the Equation Since Hannah is 7 years younger than Robert, her age can be represented as x − 7 . The sum of their ages is 61, so we can write the equation: x + ( x − 7 ) = 61
Solving for x Now, let's solve the equation for x . First, combine like terms: 2 x − 7 = 61 Next, add 7 to both sides of the equation: 2 x = 61 + 7 2 x = 68 Finally, divide both sides by 2: x = 2 68 x = 34
Finding Robert's and Hannah's Ages Now that we have the value of x , which represents Robert's age, we can find Hannah's age. Robert's age is 34 years. Hannah's age is x − 7 , so: H anna h ′ s A g e = 34 − 7 = 27 Therefore, Hannah is 27 years old.
Final Answer So, Robert is 34 years old, and Hannah is 27 years old.
Examples
Understanding how to set up and solve algebraic equations like this is useful in many real-life situations. For example, if you're trying to figure out how to split costs or resources fairly among a group, you might use similar equations. Suppose you and a friend are sharing the cost of a project, and you know your friend can contribute a certain amount less than you. By setting up an equation, you can determine exactly how much each person needs to contribute to reach the total cost.
