Problem number 20 states, there are 8 boxes in the strip shown. Numbers in adjacent boxes have sums of a or a plus 1 as shown. The number in the first box and the eighth box are both 2,021. What is the value of a? So here we have our adjacent boxes. Let's name all the values in the boxes b through g. Now let's consider these first three numbers. The first two tell us the sum of 2,021 and b is going to be equal to a. And the last two tell us that the sum of b and c is going to be a plus 1. If we subtract the second equation from the first one, the b's and the a's cancel. This gives us c minus 2,021 equals 1. Adding 2,021 to both sides, we get that c equals 2,022. Now let's apply this same logic to the next three squares. Here we would get that e is equal to 2,023. We can do this for the next three as well. Here we would get that g is equal to 2,024. Now let's just set up one last equation with the last two boxes. So it's going to be 2,024 plus 2,021 is going to be equal to a. Adding these two numbers up, we get a equals 4,045. So the question asked us, what is the value of a? The answer is 4,045. Letter e.

math problem

adjacent boxes

sum equation

value of a

solution steps