John is looking for the best deal on a smartphone that regularly costs $\$ \$ 19$. Help him compare the price of the smartphone at a store with the price on the store's website by completing the following.
(a) The store is having a sale, offering a $30 \%$ discount off the regular price of the smartphone. John also has a coupon for an additional $10 \%$ off the sale price. Ignoring tax, how much would he pay for the smartphone at the store?
(b) The store's website is offering the smartphone at a $40 \%$ discount off the regular price. But John's coupon is in-store only. It cannot be used for purchases on the website. Ignoring tax and shipping, how much would he pay for the smartphone on the store's website?
(c) Select the true statement.
John would pay less for the smartphone at the store.
John would pay less for the smartphone on the website.
John would pay the same amount at the store and on the website.
Answer
\(\boxed{\text{Therefore, the true statement is 'John would pay less for the smartphone on the website.'}}\)
Step 1 ：Let's denote the regular price of the smartphone as \(P\), which is \$199.
Step 2 ：The store is offering a 30% discount, so the sale price at the store would be \((1 - 0.3)P = 0.7P\).
Step 3 ：John also has a coupon for an additional 10% off the sale price, so the final price he would pay at the store would be \((1 - 0.1)(0.7P) = 0.63P\).
Step 4 ：Substituting \(P = 199\) into the equation, we get the final price at the store as \(0.63 \times 199 = \$125.37\).
Step 5 ：The store's website is offering a 40% discount off the regular price, so the price on the website would be \((1 - 0.4)P = 0.6P\).
Step 6 ：Substituting \(P = 199\) into the equation, we get the price on the website as \(0.6 \times 199 = \$119.40\).
Step 7 ：Comparing the two prices, we find that \$119.40 (website) < \$125.37 (store).
Step 8 ：\(\boxed{\text{Therefore, the true statement is 'John would pay less for the smartphone on the website.'}}\)
