Alvin, Calvin and Melvin each have some positive integer number of sweets. Alvin has fewer sweets than Calvin, and they have 27 sweets in total. Melvin has 19 sweets more than Alvin.
What is the maximum number of sweets that they can all have in total?
A < C
A + C = 27
M = A + 19
Note that from the third relationship, to maximize M, we also have to maximize A.
From the second relationship, we want A to be maximize in a way that it is still less than C. Thus the maximum possible integer for A = 13, so that C = 14. Thus,
M = 13 + 19
M = 32
Knowing all the values, we get their sum:
13 + 14 + 32 = 59
Hope this helps~ :3
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To find the maximum number of sweets that Alvin, Calvin, and Melvin can have in total, we need to determine the possible values for Alvin's and Calvin's number of sweets.
Let's start by assigning variables to represent the number of sweets Alvin and Calvin have:
Let A represent the number of sweets Alvin has,
Let C represent the number of sweets Calvin has.
From the given information, we know that Alvin has fewer sweets than Calvin, so we can express this relationship as A < C.
We also know that the total number of sweets they have is 27, so we can write an equation to represent this: A + C = 27.
Additionally, we are told Melvin has 19 sweets more than Alvin. We can represent Melvin's number of sweets as M = A + 19.
Now, we can substitute the value of M in terms of A into the equation for the total number of sweets: A + C + (A + 19) = 27.
Simplifying the equation, we can combine like terms: 2A + C + 19 = 27.
To find the maximum number of sweets they can all have, we need to maximize the values of A and C. To do this, we need to consider the constraints of positive integer values and the relationship A < C.
We can start by setting A to the lowest possible positive integer value, which is 1. In this case, the equation becomes 2(1) + C + 19 = 27.
Simplifying the equation we get: 2 + C + 19 = 27.
Combining the terms we get: C + 21 = 27.
Subtracting 21 from both sides we get: C = 6.
So, if Alvin has 1 sweet and Calvin has 6 sweets, we can calculate Melvin's number of sweets using the equation M = A + 19, which gives us M = 1 + 19 = 20.
To find the maximum number of sweets they can all have, we add the values of A, C, and M: 1 + 6 + 20 = 27.
Therefore, the maximum number of sweets that Alvin, Calvin, and Melvin can have in total is 27.