Ayie is 7 years older than Luis. Next year, she will be one year more than twice as old as he will be. How old is she now?
A = L + 7
(A+1) = 2(L+1)+1
A = 12
Let's solve this step-by-step:
Step 1: Let's assume Luis's age as x.
Step 2: Ayie is 7 years older than Luis, so Ayie's age can be represented as (x + 7).
Step 3: Next year, Luis's age will be (x + 1), and Ayie's age will be (x + 7 + 1), which simplifies to (x + 8).
Step 4: According to the given information, Ayie's age next year will be one year more than twice as old as Luis will be next year, which can be represented as (x + 8) = 2(x + 1) + 1.
Step 5: Now, let's solve the equation:
x + 8 = 2x + 2 + 1
Subtract x from both sides
(x + 8) - x = (2x + 2 + 1) - x
8 = x + 3
Subtract 3 from both sides
8 - 3 = x + 3 - 3
5 = x
Therefore, Luis's current age is 5.
Step 6: Ayie's current age can be found by adding 7 to Luis's age:
Ayie's current age = Luis's current age + 7
Ayie's current age = 5 + 7
Ayie's current age = 12
So, Ayie is currently 12 years old.
To solve this problem, we can represent Ayie's age as x and Luis's age as y.
Given that Ayie is 7 years older than Luis, we can write the equation: x = y + 7.
Next year, Ayie will be one year more than twice as old as Luis, which can be represented as: (x + 1) = 2(y + 1) + 1.
To find Ayie's current age, we need to solve this system of equations.
Substitute the value of x from the first equation into the second equation:
(y + 7 + 1) = 2(y + 1) + 1.
Now simplify and solve for y:
y + 8 = 2y + 2 + 1,
y + 8 = 2y + 3,
8 - 3 = 2y - y,
5 = y.
Hence, Luis is currently 5 years old.
To find Ayie's current age, substitute y = 5 into the first equation:
x = 5 + 7,
x = 12.
Therefore, Ayie is currently 12 years old.