Final answer:
The problem consists of several parts, all related to determining ages based on given relationships and sums. By translating the word problems into algebraic equations and solving for unknown variables, we can find the ages of Mary, Ali, Mel, consecutive integers, and set a word problem for Lisa and Bart.
Step-by-step explanation:
To solve the question about Mary's age, let's use variables. Let's say Mary's age is m years. According to the problem, her sister's age will then be m + 7 years. Their combined ages add up to 35, so we can write the equation m + (m + 7) = 35. Solving for m gives us Mary's age.
For Ali and Mel's ages, let's define Ali's age as a years. Mel's age is said to be three years younger than twice Ali's age, which gives us 2a - 3 for Mel's age. Their ages sum up to 39, so a + (2a - 3) = 39. Solving this equation will give us Ali's and Mel's ages.
Consecutive integers: Two consecutive integers x and x + 1 add up to 131. This can be expressed as x + (x + 1) = 131. Similarly, three consecutive integers y, y + 1, and y + 2 add up to 96 can be written as y + (y + 1) + (y + 2) = 96. Solving these will find the consecutive integers.
Finally, given two numbers with a sum of 98, and the larger one being twice the smaller one minus one, we use z for the smaller number. The equation becomes z + (2z - 1) = 98. Solving for z will yield both numbers.
To create a word problem for Lisa and Bart, consider: "Lisa is a certain age, a, and her brother Bart is three years older. If the sum of their ages is five years more than twice Lisa's age, how old are they both?" This can be expressed as a + (a + 3) = 2a + 5. Solving for a will give us Lisa's age.