bought a jumbo box of candy. by the time i got home kids ate 1/4 of candy. Put groceries away and another 1/2 of what was left was eaten. Before dinner ate another 1/6 of what was left. Now there are 10 candies left. How many chocolates were in the box to begin with.
Full box = X Candy Bars,
X - X/4 = 3X/4 Candy bars left,
(1/2)(3X/4) = 3X/8 Candy bars left,
(1/6)(3X/8) = 3X/48 = X/16 Candy bars left,
X/16 = 10 Candy bars,
Multiply both sides by 16:
X = 160 Candy bars to begin with.
To find out how many chocolates were initially in the box, we can work backwards by using the information provided.
Let's go step-by-step:
1. We know that there are 10 candies left after all the consumption.
2. Before dinner, another 1/6 of what was left was eaten. This means that 5 out of 6 parts remained. Therefore, we can calculate the number of candies before dinner = 10 * 6/5 = 12.
3. Prior to putting the groceries away, half of what was left was consumed. So, the number of candies at that point = 12 * 2 = 24.
4. Lastly, 1/4 of the candy was eaten before you arrived home. This means that 3/4 remained. Therefore, we can calculate the initial number of candies = 24 * 4/3 = 32.
Hence, there were initially 32 chocolates in the box.