High School

Four whole numbers, when added three at a time, give the sums 180,197,208180,197,208 and 222222. What is the largest of the four numbers

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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