John divided his souvenir hat pins into two piles. The two piles had an equal number of pins. He gave his brother one-half of one-third of one pile. John had 66 pins left. How many pins did John originally have?
Let's solve this step by step:
Let's say the number of pins John originally had is represented by "x".
Since the two piles had an equal number of pins, each pile had "x/2" pins.
John gave his brother one-half of one-third of one pile.
This means he gave away (1/2) * (1/3) * (x/2) pins. Simplifying this expression:
(1/2) * (1/3) * (x/2) = x/12
After giving away these pins, John had 66 pins left.
So, we can write the equation:
x - (x/12) = 66
To solve for x, let's simplify the equation:
12x - x = 66 * 12
11x = 792
x = 792/11
x ≈ 72
Therefore, John originally had approximately 72 pins.
To find the number of pins John originally had, let's break down the information provided step by step.
1. John divided his souvenir hat pins into two equal piles.
So, the number of pins in each pile is the same. Let's represent the number of pins in each pile as 'x'.
2. John gave his brother one-half of one-third of one pile.
One-half of one-third can be represented as (1/2) * (1/3).
So, John gave his brother (1/2) * (1/3) * x pins from one pile.
3. After giving his brother the pins, John had 66 pins left.
Therefore, the equation becomes:
x - (1/2) * (1/3) * x = 66
To solve this equation, follow these steps:
Step 1: Simplify the equation.
x - (1/6) * x = 66
Step 2: Combine like terms on the left side.
(5/6) * x = 66
Step 3: Multiply both sides by the reciprocal of (5/6) to isolate 'x'.
x = 66 * (6/5)
x = 79.2
Since the number of pins must be a whole number, we round the value of 'x' to the nearest whole number.
Therefore, John originally had approximately 79 pins.
1/2 * 1/3 = 1/6
So if each pile had x pins to start with,
2x - 1/6 x = 66
find x, then finish it off