High School

Mr. and Mrs. Joseph work with their son on a farm raising cows. All three of them think they are gaining weight and want to weigh themselves, but the only scales they have are the ones used to weigh the cows, which can’t weigh anything less than 100 kg. The only way to use them is to weigh themselves two at a time.

- Mr. and Mrs. Joseph combine to weigh 124 kg.
- Mrs. Joseph and her son combine to weigh 140 kg.
- Mr. Joseph and his son weigh 152 kg.

How much does each family member weigh?

Answer :

Mr. Joseph weighs 68 kg, Mrs. Joseph weighs 56 kg, and their son weighs 84 kg by using equation.

Let's solve this problem step by step. We'll assign variables to represent the weights of each family member.

Let's assume Mr. Joseph weighs x kg, Mrs. Joseph weighs y kg, and their son weighs z kg.

According to the given information, we have three equations:

1. x + y = 124 (Mr. and Mrs. Joseph combined weigh 124 kg)

2. y + z = 140 (Mrs. Joseph and her son combined weigh 140 kg)

3. x + z = 152 (Mr. Joseph and his son weigh 152 kg)

To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method:

From equations 1 and 2, we can subtract equation 2 from equation 1:

(x + y) - (y + z) = 124 - 140

This simplifies to:

x - z = -16 (Equation 4)

Now, let's add equation 4 to equation 3:

(x + z) + (x - z) = 152 + (-16)

This simplifies to:

2x = 136

Dividing both sides by 2:

x = 68

Substituting the value of x back into equation 3:

68 + z = 152

Subtracting 68 from both sides:

z = 84

Now, substituting the values of x and z back into equation 2:

y + 84 = 140

Subtracting 84 from both sides:

y = 56

Therefore, Mr. Joseph weighs 68 kg, Mrs. Joseph weighs 56 kg, and their son weighs 84 kg.

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