Ratio components

[Shoppingal]

The cost to manufacture a fibreglass boat consists of $4480 for materials, $6330 for direct labour, and $2650 for overhead. Express the components as a ratio. If the ratio can't be reduced to an equivalent ratio in terms of small integers, then express it as a ratio of decimal equivalents with the smallest term set at 1. Maintain 3-figure accuracy.

$4480:$6330:$2650

x:y:z

4480:6330, 6330:2650, 4480:2650

Am I even on the right path here?

 

[soroban]

Hello, Shoppingal!

You are misinterpreting their use of the term "ratio".

The cost to manufacture a fiberglass boat consists of:
. . $4480 for materials, $6330 for labor, and $2650 for overhead.

Express the components as a ratio.
If the ratio can't be reduced to an equivalent ratio in terms of small integers,
then express it as a ratio of decimal equivalents with the smallest term set at 1.
Maintain 3-figure accuracy.

The total cost is: .\(\displaystyle \$4,\!480 + 6,\!330 + 2,\!650 \:=\:\$13,\!460\)


We have: .\(\displaystyle \begin{Bmatrix}\text{Material:} & \dfrac{4,\!480}{13,\!460} &=& \dfrac{448}{1346} \\ \\ \text{Labor:} & \dfrac{6,\!330}{13,\!460} &=& \dfrac{633}{1346} \\ \\ \text{O'head:} & \dfrac{2,\!650}{13,\!460} &=& \dfrac{265}{1346} \end{Bmatrix}\)


. . . . . .Hence: .\(\displaystyle \text{M : L : O} \;=\;448\,:\:633\,:\,265 \)


Divide by 265: .\(\displaystyle \text{M : L : O} \;=\;1.69\,:\,2.39\,:\,1\)

 

[Shoppingal]

Thank you so much.