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Discounts. We use the following formulas to solve the problems involving
discounts:
π‘«π’Šπ’”π’„π’π’–π’π’• π’‚π’Žπ’π’–π’π’•
= π’…π’Šπ’”π’„π’π’–π’π’• 𝒓𝒂𝒕𝒆(π’„π’‰π’‚π’π’ˆπ’†π’” 𝒕𝒐 𝒂 π’…π’†π’„π’Šπ’Žπ’‚π’) βˆ— π’π’“π’Šπ’ˆπ’Šπ’π’‚π’ π’‘π’“π’Šπ’„π’†
𝑺𝒂𝒍𝒆𝒔 π’‘π’“π’Šπ’„π’† = π‘Άπ’“π’ˆπ’Šπ’π’‚π’ π’‘π’“π’Šπ’„π’† βˆ’ π‘«π’Šπ’”π’„π’π’–π’π’• π’‚π’Žπ’π’–π’π’•.

Example 9. A dictionary that normally sells for $16.50 is on sale at 40% off.
a. What is the amount of discount? Answer:$6.60
b. What is the dictionary’s sale price? Answer: $9.90
Note. To find the sale price, you can also do the following:
π‘†π‘Žπ‘™π‘’ π‘π‘Ÿπ‘–π‘π‘’ = 0.6 βˆ— 16.50 = $9.90, (why?).
…………………………………………………………………………………………………………………….
The Percent of Decrease and Percent of Increase. To find the percent of
decrease we use the following formulas,
𝑷𝒓𝒆𝒄𝒆𝒏𝒕 𝒐𝒇 𝑫𝒆𝒄𝒓𝒆𝒂𝒔𝒆 =

π’‚π’Žπ’π’–π’π’• 𝒐𝒇 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆
,
π’π’“π’Šπ’ˆπ’Šπ’π’‚π’ π’π’–π’Žπ’ƒπ’†π’“

𝑷𝒓𝒆𝒄𝒆𝒏𝒕 𝒐𝒇 𝑰𝒏𝒄𝒓𝒆𝒂𝒔𝒆 =

π’‚π’Žπ’π’–π’π’• 𝒐𝒇 π’Šπ’π’„π’“π’†π’‚π’”π’†
.
π’π’“π’Šπ’ˆπ’Šπ’π’‚π’ π’π’–π’Žπ’ƒπ’†π’“

Note. In finding the percent of decrease, the original number is the larger
number, and in finding the percent of increase, the original number is the smaller
number.

Example 10. A FAX machine regularly sells for $380. The sale price is $266. Find
the percent decrease (the discount rate).
Solution. π΄π‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘‘π‘’π‘π‘Ÿπ‘’π‘Žπ‘ π‘’ = 380 βˆ’ 266 = $114,
4