Answer:
The boutique charges $64 for a wallet, and $25 for a belt.
Step-by-step explanation:
We can write two equations using the information we are given. The we solve the system of equations to find the prices.
Let w = price of 1 wallet.
Let b = price of 1 belt.
"Last month, the company sold 25 wallets and 62 belts, for a total of $3,150."
25w + 62b = 3150
"This month, they sold 78 wallets and 19 belts, for a total of $5,467."
78w + 19b = 5467
We now have the following system of 2 equations in 2 unknowns.
25w + 62b = 3150
78w + 19b = 5467
We will use the substitution method.
Solve the first equation for w.
25w + 62b = 3150
25w = -62b + 3150
w = -62/25 b + 126
Now substitute w with -62/25 b + 126 in the second equation, and solve for b.
78w + 19b = 5467
78(-62/25 b + 126) + 19b = 5467
-4836/25 b + 9828 + 19b = 5467
-4836/25 b + 19b = -4361
Multiply both sides by 25.
-4836b + 475b = -109,025
4361b = 109,025
b = 25
Now we substitute 25 for b in the first original equation and solve for w.
25w + 62b = 3150
25w + 62(25) = 3150
25w + 1550 = 3150
25w = 1600
w = 64
Answer: The boutique charges $64 for a wallet, and $25 for a belt.
