Simple equations (involving non-integral coefficients or constants): Practice Questions

Sarah had some pencils. She gave 4 pencils to her friend and now has 9 pencils left. How many pencils did she have initially?

Calculate the value of \( m \) in the equation:
\( 2.4m - 1.2m = 6.6 \)

Solve the following equation for \( x \):
\( 0.6x - 1.4 = 2.2 \)

Find the value of \( x \) in the equation:
\( x - \frac{2}{5} = 1.6 \)

Find the value of \( y \) in the equation:
\( 0.5(y - 4.2) = 3.4 \)

Solve the following equation for \( x \):
\( 2.5x + 0.8 = 3.3 \)

A farmer has \( 84 \) apples. He keeps \( 12 \) apples for himself and divides the rest equally into several boxes. If each box contains \( 9 \) apples and the number of boxes is \( y \), write an equation and find the value of \( y \).

The length of a rectangular rug is \( 2.5 \text{ m} \) more than its width \( w \text{ m} \). If \( 40\% \) of the perimeter of the rug is \( 15.6 \text{ m} \), write an equation and solve for \( w \).

A piece of string of length \( L \) cm is cut into \( 5 \) equal sections. Each section is \( 15.6 \) cm long, and there is a remaining piece of \( 4.5 \) cm left over.

a) Write an equation to represent the relationship between the total length \( L \), the length of the sections, and the leftover piece.

b) Solve the equation to find the total length of the string \( L \).

A water tank is \( \frac{1}{4} \) full. After \( 12.5 \) litres of water are added, the tank becomes \( \frac{2}{3} \) full. Let \( V \) be the total capacity of the tank in litres.

a) Write an equation in terms of \( V \) to represent the situation.

b) Solve the equation to find the value of \( V \).

c) Starting from the \( \frac{2}{3} \) full mark, how many more litres of water are needed to fill the tank completely?