Question

In a calendar a square of four number marked The sum of the numbers is 96 what are the numbers

Answer 1

Answer:

In a calendar, a square of four numbers is marked. The sum of the numbers is 80. What are the numbers?

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This is an interesting problem because it gives you seemingly minimal information.

The first thing to notice is the given fact that all the numbers are in a square of a calendar. This is very important because, although it doesn’t directly give us values for any of the numbers, it directly gives us information on the relationship between them.

In a calendar, the number directly to the right of a chosen number (let’s have it be x) will be exactly one more than x. Hence, we can assign our first two numbers the respective values of x and x+1.

Next, we jump down exactly one row from our first number, x. Because calendars show each row with exactly one row, we know that the number directly under x will be 7 more, because it is exactly a week later. This number would therefore be assigned the value of x+7.

Using the same logic we used when we found x+1, we can derive our last value: x+8. The second piece of information states that the sum of all the numbers is 80.

We plug that number in…

80 = (x) + (x+1) + (x+7) + (x+8)

Combining like terms, it follows that…

80 = 4x + 16

Subtracting 16 from both sides gives us…

64 = 4x

Dividing by 4 on both sides results in…

x = 16

Now that we have our x value, we can simply add 1, 7, and 8, respectively, to 16 to get our solution:

The set of numbers is [16, 17, 23, 24]