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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Mariana is selling her handmade jewelry online. Yesterday, she sold $9$ bracelets and $6$ necklaces, for a profit of $\$168$ . Today, she made a profit of $\$144$ by selling $6$ bracelets and $6$ necklaces. How much profit does Mariana earn from each piece? $\newline$ Mariana earns a profit of $\$\_\_\_\_$ from every bracelet and $\$\_\_\_\_$ from every necklace.

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Solve a system of equations using elimination: word problems

Full solution

Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Mariana is selling her handmade jewelry online. Yesterday, she sold

9

bracelets and

6

necklaces, for a profit of

\$168

. Today, she made a profit of

\$144

by selling

6

bracelets and

6

necklaces. How much profit does Mariana earn from each piece?

\newline

Mariana earns a profit of

\$\_\_\_\_

from every bracelet and

\$\_\_\_\_

from every necklace.

Identify Equations: Identify the equations based on the sales and profits. $\newline$ First day sale: $9$ bracelets and $6$ necklaces for $\$168$ . $\newline$ Second day sale: $6$ bracelets and $6$ necklaces for $\$144$ . $\newline$ Let $x$ be the profit from each bracelet and $y$ be the profit from each necklace.
Write Equations: Write the system of equations for the given situation. $\newline$ First day equation: $9x + 6y = 168$ $\newline$ Second day equation: $6x + 6y = 144$
Eliminate Variable: Decide which variable to eliminate. We can eliminate $y$ by subtracting the second equation from the first because they have the same coefficient for $y$ .
Subtract Equations: Subtract the second equation from the first to eliminate $y$ . $\newline$ $(9x + 6y) - (6x + 6y) = 168 - 144$ $\newline$ $9x + 6y - 6x - 6y = 168 - 144$ $\newline$ $3x = 24$
Solve for x: Solve for x. $\newline$ $3x = 24$ $\newline$ $x = \frac{24}{3}$ $\newline$ $x = 8$
Substitute $x$ : Substitute the value of $x$ into one of the original equations to solve for $y$ . Using the second day equation: $6x + 6y = 144$ $6(8) + 6y = 144$ $48 + 6y = 144$ $6y = 144 - 48$ $6y = 96$
Solve for y: Solve for y. $\newline$ $6y = 96$ $\newline$ $y = \frac{96}{6}$ $\newline$ $y = 16$

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