Maria and John are selling candy bars for a fundraiser. Candy bars can be sold in bags or individually. Maria sold 2 bags of candy bars and 10 individual candy bars. John sold 3 bags of candy bars and 6 individual candy bars. If Maria and John each sold the same number of candy bars, how many candy bars were in each bag? show all your work
Let's solve this problem by setting up equations to represent the given information:
Let B be the number of candy bars in each bag.
Let I be the number of individual candy bars sold.
According to the problem, Maria sold 2 bags and 10 individual candy bars, and John sold 3 bags and 6 individual candy bars. We can write the following equations:
2B + 10I = 3B + 6I (Both Maria and John sold the same number of candy bars)
2B - 3B = 6I - 10I
-B = -4I
Now, let's solve for B by isolating it:
-B = -4I
B = 4I
Since B represents the number of candy bars in each bag, we can conclude that there are 4 individual candy bars in each bag.
Therefore, each bag contains 4 candy bars.
Let's assume the number of candy bars in each bag as 'x'.
Maria sold 2 bags of candy bars, so the total number of candy bars she sold from the bags is 2x.
Maria also sold 10 individual candy bars.
Therefore, the total number of candy bars Maria sold is: 2x + 10.
Similarly, John sold 3 bags of candy bars, so the total number of candy bars he sold from the bags is 3x.
John also sold 6 individual candy bars.
Therefore, the total number of candy bars John sold is: 3x + 6.
Since Maria and John each sold the same number of candy bars:
2x + 10 = 3x + 6
Now, let's solve this equation step by step to find the value of 'x'.
Subtract '2x' from both sides of the equation:
10 = x + 6
Subtract '6' from both sides of the equation:
4 = x
Therefore, the number of candy bars in each bag is 4.
To determine how many candy bars were in each bag, we need to find the total number of candy bars sold by Maria and John, and then divide it by the total number of bags sold.
Maria sold 2 bags of candy bars, with each bag containing a number of candy bars. She also sold 10 individual candy bars.
John sold 3 bags of candy bars, with each bag containing a number of candy bars. He also sold 6 individual candy bars.
To find the total number of candy bars sold by Maria, we need to multiply the number of bags she sold by the number of candy bars in each bag. Similarly, we need to multiply the number of bags and individual candy bars sold by John.
Maria's total number of candy bars = (2 bags × number of candy bars in each bag) + 10 individual candy bars
John's total number of candy bars = (3 bags × number of candy bars in each bag) + 6 individual candy bars
Since both Maria and John sold the same number of candy bars, we can equate their total number of candy bars:
(2 bags × number of candy bars in each bag) + 10 individual candy bars = (3 bags × number of candy bars in each bag) + 6 individual candy bars
Simplifying this equation will allow us to solve for the unknown number of candy bars in each bag.