if lynns age is 8 years less than 15 times the age of her neice Elizabeth, if the sum of their ages is 24, what is elizabeths age?
e = Elizabeth's age
15e - 8 = Lynn's age
these two combined = 24
e + 15e - 8 = 24
16e - 8 = 24
16e - 8 + 8 = 24 + 8
16e = 32
so e = 2 and
15(2)-8 = 22
so Elizabeth is 2 and Lynn is 22.
Hope this makes sense.
Let's break down the information given step by step:
Step 1: Let's assume Elizabeth's age as "x".
Step 2: According to the given information, Lynn's age is 8 years less than 15 times Elizabeth's age:
Lynn's age = 15x - 8
Step 3: The sum of Lynn and Elizabeth's ages is 24:
Lynn's age + Elizabeth's age = 24
Substituting the values from step 2:
(15x - 8) + x = 24
Step 4: Simplify the equation:
16x - 8 = 24
Step 5: Add 8 to both sides of the equation:
16x - 8 + 8 = 24 + 8
16x = 32
Step 6: Divide both sides of the equation by 16:
16x/16 = 32/16
x = 2
Elizabeth's age, therefore, is 2 years.
To find Elizabeth's age, let's break down the problem into steps:
Step 1: Assign variables
Let's assign variables to the unknowns in the problem. Let's say Lynn's age is L, and Elizabeth's age is E.
Step 2: Translate the given information into equations
From the problem statement, we can determine the following equations:
L = 15E - 8 (Lynn's age is 8 years less than 15 times Elizabeth's age)
L + E = 24 (The sum of their ages is 24)
Step 3: Solve the equations
We have two equations with two unknowns, so we can solve this system of equations to find the values for L and E.
From the first equation, we can substitute L in terms of E into the second equation:
(15E - 8) + E = 24
16E - 8 = 24
16E = 24 + 8
16E = 32
E = 32 / 16
E = 2
Step 4: Find Elizabeth's age
From the solution, we determined that Elizabeth's age (E) is 2. Therefore, Elizabeth is 2 years old.