Select the correct answer.
Cole's age is 3 years less than his sister Tina's age, [tex]$t$[/tex]. If Cole is 18, which equation represents this situation, and how old is Tina?
A. The equation that represents this situation is [tex]$t-3=18$[/tex]. Tina is 21.
B. The equation that represents this situation is [tex]$t+3=18$[/tex]. Tina is 15.
C. The equation that represents this situation is [tex]$3-t=18$[/tex]. Tina is 21.
D. The equation that represents this situation is [tex]$-3-t=18$[/tex]. Tina is 15.
Answer (1)
Express Cole's age in terms of Tina's age: t − 3 = 18 .
Solve for Tina's age by adding 3 to both sides: t = 18 + 3 .
Calculate Tina's age: t = 21 .
The equation is t − 3 = 18 and Tina is 21 years old, so the answer is 21 .
Explanation
Understanding the Problem Let's analyze the problem. We are given that Cole's age is 3 years less than Tina's age, which we denote as t . We also know that Cole is 18 years old. We need to find the equation that represents this situation and determine Tina's age.
Formulating the Equation We can express the relationship between Cole's age and Tina's age as an equation. Since Cole's age is 3 years less than Tina's age ( t ), we can write this as:
t − 3 = 18
Solving for Tina's Age Now, we need to solve the equation for t to find Tina's age. To do this, we add 3 to both sides of the equation:
t − 3 + 3 = 18 + 3
t = 21
Comparing with Options So, Tina is 21 years old. Now, let's compare our solution with the given options. Option A states that the equation is t − 3 = 18 and Tina is 21. This matches our solution.
Examples
Understanding age differences is a common math application. For example, if you know your friend is 5 years older than you and you are 12, you can use the equation x − 5 = 12 to find your friend's age, x , which is 17. This type of problem helps in everyday situations where you need to calculate relative ages or time differences.
