Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?(1 point)
Let's let x be Tony's current age.
Andrea is 6 years younger than Tony, so Andrea's current age is x - 6.
In two years, Tony will be x + 2 years old.
In two years, Andrea will be (x - 6) + 2 = x - 4 years old.
Since Tony will be three times as old as Andrea in two years, we can write the equation: x + 2 = 3(x - 4).
Expanding the equation gives us: x + 2 = 3x - 12.
Rearranging the equation gives us: 2x = 14.
Dividing both sides by 2 gives us: x = 7.
Therefore, the linear equation that can be used to find Andrea's and Tony's current ages is: x = 7.
Let's solve this step-by-step:
Step 1: Assign variables
Let's assign variables to represent Andrea's age and Tony's age:
Let a = Tony's current age
Let b = Andrea's current age
Step 2: Translate the given information into equations
According to the first sentence, "Andrea is 6 years younger than Tony." We can write this as: b = a - 6
According to the second sentence, "In two years, Tony will be three times as old as Andrea." In two years, Tony's age will be a + 2, and Andrea's age will be b + 2. This can be written as: a + 2 = 3(b + 2)
Step 3: Simplify the equations
By expanding the equation in Step 2, we have: a + 2 = 3b + 6
Step 4: Rearrange the equations
To find Andrea's and Tony's current ages, we need to rearrange the equations in terms of a and b.
In equation 1: b = a - 6, we can rewrite it as a = b + 6.
In equation 2: a + 2 = 3b + 6, we can rewrite it as a = 3b + 4.
So, the linear equations that can be used to find Andrea's and Tony's current ages are:
a = 3b + 4
b = a - 6