High School

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A group of four children, who each weigh less than 50 kg, weigh themselves in groups of three. The recorded weights are 122 kg, 128 kg, 125 kg, and 135 kg. How much does each child weigh?

Answer :

Answer:

Let's denote the weights of the four children as A, B, C, and D. We can write the following equations based on the given information:

A + B + C = 122

A + B + D = 128

A + C + D = 125

B + C + D = 135

Now, let's add all four equations:

3(A + B + C + D) = 122 + 128 + 125 + 135

3(A + B + C + D) = 510

Divide by 3:

A + B + C + D = 170

Now, let's subtract each of the original equations from this sum:

(170 - 122) = D = 48

(170 - 128) = C = 42

(170 - 125) = B = 45

(170 - 135) = A = 35

So, the weights of the four children are:

A = 35 kg

B = 45 kg

C = 42 kg

D = 48 kg

Each child weighs less than 50 kg, as stated in the problem.

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