Question

fluorescent powder comes in 20 G vials with 12 vials in a set, each vilal a different color. so if I order 3 sets I will have 3 viles of each colorI have 496 cups of paint to fillratio of powder to paint is one part powder to five part paint I know that 3 vials of powder which is 60g= 0.2536 cups. & .2536 cups ×5 parts paint= 1.268 cups of mixture. I got this from theBecks on hereknowing this how many sets of powder do I need to buy in order to us all my paint?

Answer 1

First you need to know how many cups of powder you are going to need for the 496 cups of paint you already have

`\begin{gathered} 1\text{ CUP POWDER}\Rightarrow5\text{ CUP PAINT} \\ x\text{ CUP POWDER}\Rightarrow496\text{ CUP PAINT} \end{gathered}`

We write this as a ratio

`\begin{gathered} (x)/(496)=(1)/(5) \\ x=(496)/(5) \\ x=99.2 \end{gathered}`

for the 496 cups of paint you will need 99.2 cups of powder.

Continue by seeing how may grams there are in 99.2 cups

`\begin{gathered} 60g\Rightarrow0.2536\text{ CUPS POWDER} \\ x\Rightarrow99.2\text{ CUPS POWDER} \end{gathered}`

write it as a ratio and solve for x again.

`\begin{gathered} (x)/(99.2)=(60)/(0.2536) \\ x=23470.03155 \end{gathered}`

now find how many vials you will need

`\begin{gathered} 1\text{vial}\Rightarrow20g \\ x\Rightarrow23470.03155g \end{gathered}`

write the ratio and solve

`\begin{gathered} (x)/(23470.03155)=(1)/(20) \\ x=(23470.03155)/(20) \\ x=1173.5\approx1174 \end{gathered}`

If each sets comes with 12 sets, write the ratio and find the number of sets you will need

`\begin{gathered} 1\text{set}\Rightarrow12vials \\ \text{xsets}\Rightarrow1174vials \end{gathered}`
`\begin{gathered} (x)/(1174)=(1)/(12) \\ x=(1174)/(12) \\ x=97.83\approx98 \end{gathered}`

you will need 98 sets for this amount of paint.