Question

zara sells keychains and bookmarks online. one day she sold 8 keychains and 10 bookmarks and made $256.76. two days later she sold 48 keychains and 18 bookmarks and made $719.88. how much is each keychain and bookmark individually? a. each keychain costs $7.67 and each bookmark costs $19.54. b. each keychain costs $12.34 and each bookmark costs $6.34. c. each keychain costs $8.76 and each bookmark costs $18.34. d. each keychain costs $13.23 and each bookmark costs $19.53.

Explanation:

Step1: Define variables

Let \( x \) be the cost of one keychain and \( y \) be the cost of one bookmark.
From the first day: \( 8x + 10y = 256.76 \)
From the second day: \( 48x + 18y = 719.88 \)

Step2: Simplify the first equation

Divide the first equation by 2: \( 4x + 5y = 128.38 \) (Equation 1)

Step3: Simplify the second equation

Divide the second equation by 6: \( 8x + 3y = 119.98 \) (Equation 2)

Step4: Multiply Equation 1 by 2

\( 8x + 10y = 256.76 \) (Equation 3)

Step5: Subtract Equation 2 from Equation 3

\( (8x + 10y) - (8x + 3y) = 256.76 - 119.98 \)
\( 7y = 136.78 \)
\( y = \frac{136.78}{7} = 19.54 \)

Step6: Substitute \( y = 19.54 \) into Equation 1

\( 4x + 5(19.54) = 128.38 \)
\( 4x + 97.7 = 128.38 \)
\( 4x = 128.38 - 97.7 \)
\( 4x = 30.68 \)
\( x = \frac{30.68}{4} = 7.67 \)

Answer:

A. Each keychain costs $7.67 and each bookmark costs $19.54.