Question

Pat made a total of $48$ pottery plates and cups. If she made twice as many plates as cups. How many plates did she make?

Answer 1

Calculate the number of plates made.

Let the number of cups made be $x$.

Let the number of plates made be $y$.

Given that the total number of cups and plates made are $48$.

Add $x$ and $y$ and put it to equal to $48$.

$\mathrm{x}+\mathrm{y}=48...\left(1\right)$

Also, she made twice as many plates as cups.

Multiply $x$ by $2$ and put it equal to $y$.

$\mathrm{y}=2\mathrm{x}...\left(2\right)$

Substitute $2x$ for $y$ in the equation $x+y=48.$

$$\begin{gathered} \mathrm{x}+2\mathrm{x}=48 \\ \Rightarrow 3\mathrm{x}=48 \\ \Rightarrow \mathrm{x}=\frac{48}{3} \\ \therefore \mathrm{x}=16 \end{gathered}$$

Substitute $16$ for $x$ in the equation $y=2x$.

$$\begin{gathered} y=2\times 16 \\ \therefore y=32 \end{gathered}$$

Hence, the number of plates made is $32$.