n a calendar, a square of 4 numbers is marked. The sum of the numbers
is 76. What are the numbers /
Answers
Answer:
16,17,23,24
Step-by-step explanation:
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]
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