Final answer:
The equation given by Jada uses the variable 'x' to represent a base age, with other terms representing the ages of additional individuals relative to this base age. Terms like (x+3) and (x-2) indicate ages 3 years older and 2 years younger than the base age, respectively. Simplifying the equation allows us to solve for 'x' to determine the base age, which in this case is 13.
Step-by-step explanation:
The equation Jada writes, (x) + (x+3) + (x−2) + 3(x+3) − 1=87, represents the sum of the ages of possibly four individuals. The variable x is likely representing the age of the youngest person or a base age from which the other ages are calculated. Each term of the equation reveals the relationship of other individuals' ages to this base age. Specifically, the terms (x+3) and (x−2) likely represent the ages of individuals who are 3 years older and 2 years younger than the base age, respectively. The term 3(x+3) suggests that there are three individuals who are each 3 years older than the base age. The minus 1 at the end of the equation could represent a correction or adjustment factor.
By simplifying this equation, we can solve for x to find the base age. The approach to solving this equation is as follows:
First combine like terms:
- Combine all the x terms together: x + x + x + 3x = 6x.
- Sum up the constants: 3 - 2 + 9 - 1 = 9.
- Now the equation simplifies to 6x + 9 = 87.
- Subtract 9 from both sides: 6x = 78.
- Finally, divide by 6 to solve for x: x = 13.
Therefore, the base age x is 13 years old. You can then use this value to calculate the specific ages of the other individuals described by the other terms in the original equation.