Question

A plate with 15 blocks on it weighs 140 g. A plate with 5blocks on it weighs 90 g. The blocks all weigh the same.How much does the plate weigh?

Answer 1

Let a denotes the weight of a plate

Let b denotes the weight of a blocks

We are given

`\begin{gathered} a+15b=140 \\ a+5b=90 \end{gathered}`

We want to find a

Solution

The above equation is a simultaneous equation

and we want to find a

`\begin{gathered} a+15b=140\text{ eqn(1)} \\ a+5b=90\text{ eqn(2)} \end{gathered}`

we multiply eqn(2) by 3 throughout, so that the new system of equations will be

`\begin{gathered} a+15b=140\ldots\ldots\ldots(1) \\ 3a+15b=270\ldots\ldots\ldots(2) \end{gathered}`

Now, eqn(2) - eqn(1)

`\begin{gathered} (3a-a)+(15b-15b)=270-140 \\ 2a+0=130 \\ 2a=130 \\ a=(130)/(2) \\ a=65 \end{gathered}`

The plate weigh 65g