Question

A) find the value of x
B) find the value of y

Answer 1

a) x = 9.

b) y = 61.

Explanation:

As the 2 weighing scales balance:

4 + 4x = 31 + x

3x = 31 - 4 = 27

x = 9.

Also 4 + 4x + x + 31 = y + 2x + 1

Substituting for x:

4 + 4(9) + 9 + 31 = y + 2(9) + 1

80 = y + 19

y = 80 - 19 = 61.

Answer 2

x = 9

y = 61

Explanation:

The main scales are balanced.

The left side of the main scales comprises another scale, which is also balanced.

From this and the values given, we can construct two equations.

Equation 1

Balancing the scales on the left of the main scales:

⇒ 4 + 4x = 31 + x

Solving this for x:

⇒ 4 + 4x - 4 = 31 + x - 4

⇒ 4x = 27 + x

⇒ 4x - x = 27 + x - x

⇒ 3x = 27

⇒ 3x ÷ 3 = 27 ÷ 3

⇒ x = 9

Equation 2

Balancing the main scales:

4 + 4x + 31 + x = y + 1 + 2x

Rearranging to make y the subject:

⇒ 5x + 35 = y + 1 + 2x

⇒ 5x + 35 - 1 = y + 1 + 2x - 1

⇒ 5x + 34 = y + 2x

⇒ 5x + 34 - 2x = y + 2x - 2x

⇒ 3x + 34 = y

Substituting the found value of x (from Equation 1) and solving for y:

⇒ y = 3(9) + 34

⇒ y = 27 + 34

⇒ y = 61

Therefore:

• x = 9
• y = 61