Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 05, 2023

Find the ratio of colored pencils to markers for art supply packages A and B, given the ratios 5:2 and 4:3 respectively.

STEP 1

Assumptions1. Package A has a colored pencil to marker ratio of5 to. Package B has a colored pencil to marker ratio of4 to3

STEP 2

We will first complete the ratio table for Package A. The ratio5 to2 means that for every5 colored pencils, there are2 markers.We can write this as $\begin{array}{|c|c|} \hline\text{Coloredencils (Package A)} & \text{Markers (Package A)} \\ \hline5 &2 \\ \hline\end{array}$

STEP 3

Now, we will add more rows to the table by multiplying the number of colored pencils and markers by the same number. Let's multiply by2,3, and.

STEP 4

Calculate the number of colored pencils and markers when multiplied by2.
$\begin{array}{|c|c|} \hline\text{Coloredencils (Package A)} & \text{Markers (Package A)} \\ \hline &2 \\ \times2 &2 \times2 \\ \hline\end{array}$

STEP 5

Calculate the number of colored pencils and markers when multiplied by3.
$\begin{array}{|c|c|} \hline\text{Coloredencils (Package A)} & \text{Markers (Package A)} \\ \hline5 &2 \\ 5 \times2 &2 \times2 \\ 5 \times3 &2 \times3 \\ \hline\end{array}$

STEP 6

Calculate the number of colored pencils and markers when multiplied by4.
$\begin{array}{|c|c|} \hline\text{Coloredencils (Package A)} & \text{Markers (Package A)} \\ \hline5 &2 \\ 5 \times2 &2 \times2 \\ 5 \times3 &2 \times3 \\ 5 \times4 &2 \times4 \\ \hline\end{array}$

STEP 7

Now, we will complete the ratio table for Package B. The ratio4 to3 means that for every4 colored pencils, there are3 markers.We can write this as $\begin{array}{|c|c|} \hline\text{Coloredencils (Package B)} & \text{Markers (Package B)} \\ \hline4 &3 \\ \hline\end{array}$

STEP 8

Now, we will add more rows to the table by multiplying the number of colored pencils and markers by the same number. Let's multiply by2,3, and4.

STEP 9

Calculate the number of colored pencils and markers when multiplied by2.
$\begin{array}{|c|c|} \hline\text{Coloredencils (Package B)} & \text{Markers (Package B)} \\ \hline4 &3 \\ 4 \times2 &3 \times2 \\ \hline\end{array}$

STEP 10

Calculate the number of colored pencils and markers when multiplied by3.
$\begin{array}{|c|c|} \hline\text{Coloredencils (Package B)} & \text{Markers (Package B)} \\ \hline4 &3 \\ 4 \times2 &3 \times2 \\ 4 \times3 &3 \times3 \\ \hline\end{array}$

STEP 11

Calculate the number of colored pencils and markers when multiplied by4.
$\begin{array}{|c|c|} \hline\text{Coloredencils (Package B)} & \text{Markers (Package B)} \\ \hline4 &3 \\ 4 \times &3 \times \\ 4 \times3 &3 \times3 \\ 4 \times4 &3 \times4 \\ \hline\end{array}$ The completed ratio tables for Package A and Package B arePackage A $\begin{array}{|c|c|} \hline\text{Coloredencils (Package A)} & \text{Markers (Package A)} \\ \hline5 & \\ 10 &4 \\ 15 &6 \\ 20 &8 \\ \hline\end{array}$ Package B $\begin{array}{|c|c|} \hline\text{Coloredencils (Package B)} & \text{Markers (Package B)} \\ \hline4 &3 \\ 8 &6 \\ &9 \\ 16 & \\ \hline\end{array}$

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