At present, Tara's father is 42 years older than Tara. 5 years ago, her father was 4 times as old as her. Solve for y, Tara's current age.
f = y+42
f-5 = 4(y-5)
To solve this problem, we need to set up equations based on the given information and then solve for Tara's current age, denoted as y.
Let's use the following steps:
Step 1: Set up equations based on the given information:
At present, Tara's father is 42 years older than Tara.
This can be expressed as: Father's age = Tara's age + 42
5 years ago, Tara's father was 4 times as old as her.
This can be expressed as: Father's age 5 years ago = 4 * (Tara's age 5 years ago)
Step 2: Write equations based on the given information:
Father's age = Tara's age + 42
Father's age 5 years ago = 4 * (Tara's age 5 years ago)
Step 3: Express Tara's current age in terms of y (Tara's current age):
Tara's age = y
Step 4: Rewrite the equations using y:
Father's age = y + 42
Father's age 5 years ago = 4 * (y - 5)
Step 5: Set up an equation by substituting the expressions of father's age:
Father's age = Father's age 5 years ago + 5 (because 5 years ago is 5 years before the present)
(y + 42) = 4 * (y - 5) + 5
Step 6: Solve the equation for y:
Expand the equation:
y + 42 = 4y - 20 + 5
Combine like terms:
y + 42 = 4y - 15
Move the variables to one side and the constants to the other side:
y - 4y = -15 - 42
-3y = -57
Divide both sides by -3 to isolate y:
y = -57 / -3
y = 19
Step 7: Interpret the result:
Tara's current age, y, is equal to 19.
Therefore, Tara is currently 19 years old.