Lin is shopping for a couch with her dad and hears him ask the salesperson, "How much is your commission?" The salesperson says that her commission is \( 5 \frac{1}{2} \% \) of the selling price. a. How much commission will the salesperson earn by selling a couch for \( \$ 495 \) ? b. How much money will the store get from the sale of the couch?

To find out how much commission the salesperson will earn on a couch sold for $495 at a commission rate of \( 5 \frac{1}{2} \% \), we first convert the mixed number to an improper fraction. \( 5 \frac{1}{2} \% \) is equivalent to \( \frac{11}{2} \% \), which converts to a decimal as follows: \[ \frac{11}{2} \% = 5.5\% = 0.055 \] Now, calculate the commission: \[ \text{Commission} = \$495 \times 0.055 = \$27.225 \] Thus, the salesperson earns approximately \$27.23. Next, to find out how much money the store gets from the sale, we simply subtract the commission from the selling price: \[ \text{Store's Earnings} = \$495 - \$27.225 = \$467.775 \] So, the store will get approximately \$467.78 from the sale of the couch.