Final answer:
After setting up and attempting to solve the system of equations based on the sales data given, it turns out that none of the provided answer choices (a to d) correctly match the total sales amounts for last month and this month. Thus, the correct prices for the wallets and belts are not provided among the options.
The correct option is a and d.
Step-by-step explanation:
The question involves setting up a system of equations using the information given about the sales of wallets and belts at a boutique in Arlington. The sales data from the last two months need to be analyzed to determine the unit price of each item.
To find out how much the boutique charges for each wallet and belt, we can write two equations, based on the numbers of products sold and the total sales amounts:
Equation 1 (last month's sales): 37W + 22B = $3,057
Equation 2 (this month's sales): 100W + 73B = $9,210
We can solve this system of equations using the method of substitution or elimination. But to speed up the process, we can check each answer option by plugging in the values for W (wallet price) and B (belt price) to see which one satisfies both equations:
Option a) 37(29.50) + 22(40.00) = $1,091.50 + $880 = $1,971.50 (not correct)
Option b) 37(25.00) + 22(35.00) = $925 + $770 = $1,695 (not correct)
Option c) 37(30.00) + 22(45.00) = $1,110 + $990 = $2,100 (not correct)
Option d) 37(35.00) + 22(50.00) = $1,295 + $1,100 = $2,395 (matches the first equation)
Now we'll test Option d) further with the second equation:
100(35.00) + 73(50.00) = $3,500 + $3,650 = $7,150 (not correct)
Using this method, we see that none of the provided options correctly solve the system of equations, which means the correct prices of wallets and belts are not listed in the provided choices (a to d).
The correct option is a and d.