To help raise funding for homeless’ Thanksgiving Dinner, Christina and her friends sell chocolate bars during lunch time. They sold 2/5 of the total on day one, and sold 1/2 of the leftover on day two. On day three, they sold 1/3 less than sales on day one, and are left with 50 leftover bars. What was the total chocolate bars they had at the beginning?
2/5 x + 1/5 x + 4/15 x + 50 = x
375
To find the total number of chocolate bars they had at the beginning, we need to add up the number of bars sold on each day and the number of leftover bars on the last day.
Let's break down the information given:
On day one, they sold 2/5 of the total number of chocolate bars. This means they sold (2/5) * total bars on day one.
On day two, they sold 1/2 of the leftover bars from day one. So, the number of bars sold on day two is (1/2) * (remaining bars from day one).
On day three, they sold 1/3 less than the number of bars sold on day one. This means they sold (1 - 1/3) * bars sold on day one.
Finally, we know that there were 50 leftover bars on the last day.
We can set up an equation:
(2/5) * total bars + (1/2) * (2/5) * total bars + (2/3) * (2/5) * total bars + 50 = total bars
To solve this equation for the total number of bars, we'll need to simplify the equation and isolate the variable.
Let's calculate the values:
(2/5) * total bars = (2/5) * total bars
(1/2) * (2/5) * total bars = (1/10) * total bars
(2/3) * (2/5) * total bars = (4/15) * total bars
Now we can rewrite the equation:
(2/5) * total bars + (1/10) * total bars + (4/15) * total bars + 50 = total bars
Combining the fractional terms:
(6/15) * total bars + (1/10) * total bars + 50 = total bars
Multiplying each term by 30 to eliminate the denominators:
6 * total bars + 3 * total bars + 1500 = 30 * total bars
Combining like terms:
9 * total bars + 1500 = 30 * total bars
Subtracting 9 * total bars from both sides:
1500 = 21 * total bars
Dividing both sides by 21:
total bars = 1500 / 21
Simplifying:
total bars = 71.43
Since we're counting whole chocolate bars, we need to round up to the nearest whole number:
total bars ≈ 72
So, they had approximately 72 chocolate bars at the beginning.