Answer :
The given statement is “Four whole numbers, when added three at a time, give the sums 180, 197, 208 and 222. The largest of the four numbers is D, which is equal to A + D = 27.
Here, the largest of the four numbers is required to be determined. A word has a distinct meaning, and a well-thought-out sentence is built using the right words. Words that are carefully chosen can deliver a powerful message, and when limited to a word count, every word becomes important.
Four whole numbers, when added three at a time, give the sums 180, 197, 208, and 222. Let's say that the four numbers are A, B, C, and D.
Now, we can write the following equations:
A + B + C = 180
B + C + D = 197
A + C + D = 208
A + B + D = 222
Adding all four equations, we get:
2(A + B + C + D) = 807
⇒ A + B + C + D = 403
Substituting this value in all the above equations, we can get the values of A, B, C, and D.
Now, we will consider the third equation A + C + D = 208 and substitute the value of A + B + C + D in the equation, which is 403.
A + C + D = 208
⇒ 403 - B = 208
⇒ B = 403 - 208 = 195
Now, the largest number can be determined from the fourth equation:
A + B + D = 222
⇒ A + 195 + D = 222
⇒ A + D = 27
So, the largest of the four numbers is D, which is equal to A + D = 27.
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