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)
Since Andrea is 6 years younger than Tony, we can express their ages as follows:
Tony's current age: a
Andrea's current age: a - 6
In two years, Tony will be three times as old as Andrea. We can express this using the equation:
a + 2 = 3(a - 6 + 2)
Simplifying the equation, we get:
a + 2 = 3(a - 4)
So, the correct linear equation is:
a + 2 = 3(a - 4)
Let's solve this step by step:
Step 1: Define the variables:
Let a be Tony's current age.
Let t be Andrea's current age.
Step 2: Translate the given information into equations:
"Andrea is 6 years younger than Tony":
t = a - 6
"In two years, Tony will be three times as old as Andrea":
Tony's age in 2 years = a + 2
Andrea's age in 2 years = t + 2
According to the second statement, Tony's age in two years will be three times Andrea's age, so we can express this as an equation:
a + 2 = 3(t + 2)
Step 3: Simplify the equation:
a + 2 = 3t + 6
Now we have a system of equations:
t = a - 6
a + 2 = 3t + 6
These equations can be used to find Andrea's and Tony's current ages.