Anna has a bag of chocolates and a bag of caramels. If she gives an equal amount of each type of candy to each of her 7 friends, she is left with 5 chocolates and 1 caramel. Which of the following could be the total number of chocolates and caramels that were in the two bags?
More data needed.
12 chocolates and 8 caramels is one possibility.
19 chocolates and 15 caramels is another.
a) 54
b) 55
c) 56
d) 57
e) 58
(7*3)+5 = 26 chocolates and (7*3)+1 = 22 caramels = ?
To solve this problem, we'll use algebra. Let's assume the number of chocolates in the bag is represented by "C" and the number of caramels is represented by "K".
From the given information, we know that if Anna gives an equal amount of each type of candy to each of her 7 friends, she is left with 5 chocolates and 1 caramel.
So, we can set up the following two equations:
1. C = 7x + 5
2. K = 7x + 1
Here, "x" represents the number of candies given to each friend.
Now, we need to find a combination of C and K that satisfies both equations.
Let's check the answer choices using the given equations:
a) C = 19 and K = 8:
If we substitute the values of C and K into the equations, we have:
19 = 7x + 5 (Equation 1)
8 = 7x + 1 (Equation 2)
We can solve Equation 1 to find x:
19 - 5 = 7x
14 = 7x
x = 2
Now, we substitute x=2 in Equation 2:
8 = 7(2) + 1
8 = 14 + 1
8 = 15 (not true)
Therefore, (a) is not a valid answer.
b) C = 23 and K = 8:
If we substitute the values of C and K into the equations, we have:
23 = 7x + 5 (Equation 1)
8 = 7x + 1 (Equation 2)
We can solve Equation 1 to find x:
23 - 5 = 7x
18 = 7x
x = 18/7
Since x is not a whole number, (b) is not a valid answer.
c) C = 33 and K = 8:
If we substitute the values of C and K into the equations, we have:
33 = 7x + 5 (Equation 1)
8 = 7x + 1 (Equation 2)
We can solve Equation 1 to find x:
33 - 5 = 7x
28 = 7x
x = 4
Now, we substitute x=4 in Equation 2:
8 = 7(4) + 1
8 = 28 + 1
8 = 29 (not true)
Therefore, (c) is not a valid answer.
d) C = 48 and K = 8:
If we substitute the values of C and K into the equations, we have:
48 = 7x + 5 (Equation 1)
8 = 7x + 1 (Equation 2)
We can solve Equation 1 to find x:
48 - 5 = 7x
43 = 7x
x = 43/7
Since x is not a whole number, (d) is not a valid answer.
e) C = 53 and K = 8:
If we substitute the values of C and K into the equations, we have:
53 = 7x + 5 (Equation 1)
8 = 7x + 1 (Equation 2)
We can solve Equation 1 to find x:
53 - 5 = 7x
48 = 7x
x = 48/7
Since x is not a whole number, (e) is not a valid answer.
After checking all the answer choices, none of them yield a valid solution that satisfies both equations.
Therefore, we cannot determine the total number of chocolates and caramels based on the given information.