Question

scarlet and paula are on a vacation. they went to a store to buy some souvenirs for their friends back home. scarlet bought three pairs of sunglasses and two shirts for \\$81 and paula bought one pair of sunglasses and five shirts for \\$105.

what is the cost of one pair of sunglasses and one shirt?

• the cost of one pair of sunglasses is \\$18 and the cost of one shirt is \\$15.
• the cost of one pair of sunglasses is \\$15 and the cost of one shirt is \\$18.
• the cost of one pair of sunglasses is \\$12 and the cost of one shirt is \\$23.
• the cost of one pair of sunglasses is \\$23 and the cost of one shirt is \\$12.

Explanation:

⚡ Using what you learned: Solving Systems by Elimination (Addition)

Step 1: Define variables and set up equations

Let \( x \) be the cost of one pair of sunglasses and \( y \) be the cost of one shirt.

$$
LATEXBLOCK0
$$

Step 2: Multiply the second equation to align coefficients

Multiply the second equation by \(-3\):

$$ -3(x + 5y) = -3(105) \implies -3x - 15y = -315 $$

Step 3: Add the equations to eliminate \( x \)

$$
LATEXBLOCK1
$$

$$ y = \frac{-234}{-13} = 18 $$

Step 4: Substitute \( y \) back to find \( x \)

$$ x + 5(18) = 105 $$

$$ x + 90 = 105 $$

$$ x = 15 $$

Answer:

The cost of one pair of sunglasses is $15** and the cost of one shirt is **$18.