Question

Why do you multiply both sides by 4/3 next?

Answer 1

see explanation

Explanation:

let x be the number of candles , then

`(3)/(4)` x + 3 = 12 ( subtract 3 from both sides )

`(3)/(4)` x = 9 ( multiply both sides by 4 to clear the fraction )

3x = 36 ( divide both sides by 3 )

x = 12

that is 12 candles were shipped

now, multiplying by 4 then dividing by 3 is equivalent to

multiplying both sides by
`(4)/(3)`

Answer 2

Marvin Shipped 12 Candles

━━━━━━━━━━━━━━━━━━━━━━

`\begin{gathered} \\ \; \; \sf{\rm{Given \: {\begin{cases} \sf Total_((Weight)) = 12 \; pounds \\ \\ \sf Weight_((Box)) = 3 \; pounds \\ \\ \sf Weight_((Each \; Candle)) = (3)/(4) \; pound \end{cases}}}} \\ \\ \end{gathered}`

Let ::

Number Of Candles = x

ㅤ

Then ::

Weight Of All Candles

`\begin{gathered} \\ \; \; \sf{:\longmapsto{Weight_((Each \; Candle)) * Number_((Candle))}} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; \sf{:\longmapsto{(3)/(4) * x}} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; \sf{:\longmapsto{(3x)/(4)}} \\ \\ \end{gathered}`

Now ::

Candles Marvin Shipped

`\begin{gathered} \\ \; \; \sf{:\longmapsto{Weight_((All \; Candles)) + Weight_((Box)) = Total_((Weight))}} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; \sf{:\longmapsto{(3x)/(4) + 3 = 12}} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; \sf{:\longmapsto{(3x)/(4) = 12 - 3}} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; \sf{:\longmapsto{(3x)/(4) = 9}} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; \sf{:\longmapsto{3x = 9 * 4}} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; \sf{:\longmapsto{3x = 36}} \\ \\ \end{gathered}`

`\begin{gathered} \\ \; \; \sf{:\longmapsto{x = \cancel{(36)/(3)}}} \\ \\ \end{gathered}`

`\begin{gathered} \; \; :\longmapsto{\boxed{\orange{\frak{x = 12}}}} \; \pmb{\bigstar} \\ \\ \end{gathered}`

`\bf{\pmb{\underline{\rule{170pt}{5pt}}}}`