Question

An apparel shop sells skirts for $45 and blouses for $35. It's 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:

The skirts left in the store are 260 and blouses left are 270.

Step-by-step explanation:

Given:

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

The worth of entire stock is $51,750.

Now, to find how many skirts and blouses are left in the store.

Let the total price of skirts be $x.$

And let the total price of blouses be $y.$

So, price of the entire stock is:

$x+y=51,750\\\\y=51750-x \ \ \ \ .....(1)$

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

Now, the price of the half skirts and two-thirds of the blouses:

$\frac{1}{2} x+\frac{2}{3} y=30,600\\\\\frac{x}{2} +\frac{2y}{3} =30,600$

Substituting the value of $y$ from equation (1) we get:

$\frac{x}{2}+\frac{2\times(51750-x) }{3}=30,600\\\\\frac{x}{2}+\frac{(103500-2x) }{3}=30,600\\\\\frac{ 3x+207000-4x}{6}=30,600$

Multiplying both sides by 6 we get:

$3x+207000-4x=183600$

$207000-x=183600$

Subtracting both sides by 207000 we get:

$-x=183600-207000\\\\-x=-23400\\\\x=23400.$

The total price of skirts = $23,400.

By substituting the value of $x$ in equation (1) we get:

$y=51750-x\\\\y=51750-23400\\\\y=28350.$

The total price of blouses = $28,350.

The sale price of a skirt = $45.

The sale price of a blouse = $35.

Now, to get the total number of skirts and blouses of the stock:

The total number of skirts in the stock = The total price of skirts ÷ the sale price of a skirt.

                                                                $=23,400\div 45\\\\=520.$

The total number of skirts in the stock = 520.

The total number of blouses in the stock = The total price of blouses ÷ the sale price of a blouse.

                                                                    $=28350\div 35\\\\= 810.$

The total number of blouses in the stock = 810.

In the shop only half of the skirts and two-thirds of the blouses are sold.

Now, to get the skirts left in the store:

$520-\frac{1}{2}\ of\ 520 \\\\=520-0.5\times 520\\\\=520-260\\\\=260.$

Thus, 260 skirts are left in the store.

Now, to get the blouses left in the store:

$810-\frac{2}{3} \ of\ 810\\\\=810-\frac{2}{3} \times 810\\\\=810-\frac{1620}{3} \\\\=810-540\\\\=270.$

Hence, 270 blouses are left in the store.

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

Answer 2

Answer:

The skirts left in the store are 260 and blouses left are 270.

Step-by-step explanation:

Given:

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

The worth of entire stock is $51,750.

Now, to find how many skirts and blouses are left in the store.

Let the total price of skirts be

And let the total price of blouses be

So, price of the entire stock is:

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

Now, the price of the half skirts and two-thirds of the blouses:

Substituting the value of  from equation (1) we get:

Multiplying both sides by 6 we get:

Subtracting both sides by 207000 we get:

The total price of skirts = $23,400.

By substituting the value of  in equation (1) we get:

The total price of blouses = $28,350.

The sale price of a skirt = $45.

The sale price of a blouse = $35.

Now, to get the total number of skirts and blouses of the stock:

The total number of skirts in the stock = The total price of skirts ÷ the sale price of a skirt.

                                                               

The total number of skirts in the stock = 520.

The total number of blouses in the stock = The total price of blouses ÷ the sale price of a blouse.

                                                                   

The total number of blouses in the stock = 810.

In the shop only half of the skirts and two-thirds of the blouses are sold.

Now, to get the skirts left in the store:

Thus, 260 skirts are left in the store.

Now, to get the blouses left in the store:

Hence, 270 blouses are left in the store.

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

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