Question

Sales An apparel shop sells skirts for $45 and blouses for $35. Its entire stock is worth $51,750. But sales are slow and only half the skirts and two-thirds of the blouses are sold, for a total of $30,600. How many skirts and blouses are left in the store?

Answer 1

Answer:

260 skirts and 270 blouses are left in the store after the sale.

Step-by-step explanation:

Let x be the number of skirts and y be the number of blouses.

An apparel shop sells skirts for $45 and blouses for $35

Cost of entire stock = $51,750

Thus, we can write the equation,

$45x + 35y = 51750$

Half the skirts and two-thirds of the blouses are sold for a total of $30,600.

Thus, we can write the equation,

$45(\dfrac{x}{2}) + 35(\dfrac{2y}{3}) = 30600\\\\135x + 140y = 183600$

Solving the two equations by elimination method, we have,

$135x + 140y-(135x + 105y) = 183600 - 155250\\35y = 28350\\\\y = \dfrac{28350}{35} =810\\\\x = \dfrac{51750-35(810)}{45} = 520$

Thus, there were 520 skirts and 810 blouses in the store.

Skirt left =

$520-\dfrac{520}{2} = 260$

Blouses left =

$810 - \dfrac{2}{3}\times 810 = 270$

Thus, 260 skirts and 270 blouses are left in the store after the sale.