Question

A boutique specializes in leather goods for men. Last month, the company sold 20 wallets and 53 belts, for a total of $3,517. This month, they sold 28 wallets and 97 belts, for a total of $6,041. How much does the boutique charge for each item?

Answer 1

Answer:

25 wallets and 53 belts

Step-by-step explanation:

Firstly, we need to represent the amount with variables ( alphabets)

Let the amount charged for a belt be $b and the amount charged for a wallet be $w.

Now, we were told that last month, the company sold 20 wallets and 53 belts for 3,417.

Now if 1 wallet costs $w, 20 wallets would cost $20w

In a likewise manner, if 1 belt costs $b , 53 belts will cost $53b.

Now since we know the total cost of both equals 3,417 , this mean

$20w + $53b = $3,417

First equation.

In likewise manner,

$28w + $97b = $6,041

Second equation

This simply shows we have 2 equations to solve simultaneously.

From equation 1, we can see that

20w = 3,417 - 53b

Equation 2 can also be expressed as:

1.4(20w) + 97b = 6041

We now substitute for 20w in equation 2.

1.4(3,417 - 53b) + 97b = 6041

4783.8 - 74.2b + 97b = 6041

97b - 74.2b = 6041 - 4783.8

22.8b = 1257.2

b = 1257.2/22.8 = apprx 55 belts

20w = 3,417 - 53b

Substitute for b here.

20w = 3417 - 53(55)

20w = 3417 - 2915

20w = 502

w = 502/20 = apprx 25