SAMPLE College Math

‭Now, multiply both numerator and denominator by 5 so that the denominator becomes 100.‬ ‭1 ‭2 5 0 ‬ ‬ * ‭5 ‭5 ‬ ‬ = ‭1 ‭7 0 5 0 ‬ ‬ ‭Let‬‭us‬‭consider‬‭another‬‭case,‬‭where‬‭you‬‭have‬‭scored‬‭65‬‭out‬‭of‬‭75.‬‭Now‬‭in‬‭this‬‭case,‬‭multiply‬‭and‬‭divide‬ ‭the fraction by 100 and substitute the 100 in denominator as % sign and simplify the same:‬ ‭6 ‭7 5 5 ‬ ‬ * ‭1‭1 00 00 ‬‬ = ‭6 ‭7 5 5 ‬ ‬ * ‭100‬‭‬‭%‬ = ‭86‬. ‭67%‬ ‭Sometimes‬‭we‬‭need‬‭to‬‭find‬‭the‬‭percentage‬‭of‬‭a‬‭particular‬‭value--for‬‭example,‬‭calculating‬‭a‬‭10%‬‭tip‬‭on‬‭a‬ ‭restaurant check of $460. To do this, find 10 percent of $460. Mathematically,‬ ‭1 ‭1 0 0 0 ‬ ‬ * ‭460‬ = ‭$46‬ ‭B. Discounts, Markups, and Taxation‬ ‭We‬ ‭all‬ ‭are‬ ‭familiar‬ ‭with‬ ‭the‬ ‭terms‬ ‭like‬ ‭‘discounts,‬ ‭markups,‬ ‭and‬ ‭taxation.’‬ ‭Calculating‬ ‭these‬ ‭amounts‬ ‭makes‬‭use‬‭of‬‭percentage‬‭concepts‬‭in‬‭the‬‭previous‬‭section.‬‭For‬‭example,‬‭you‬‭go‬‭to‬‭a‬‭grocery‬‭store‬‭where‬ ‭you‬ ‭see‬ ‭an‬‭offer‬‭that‬‭if‬‭you‬‭spend‬‭over‬‭$500,‬‭you‬‭get‬‭a‬‭5%‬‭discount.‬‭If,‬‭for‬‭example,‬‭you‬‭spend‬‭$570,‬ ‭then you can find the discount amount by finding 5% OF the total, that is:‬ ‭1 ‭5 0 ‬ 0‬ * ‭570‬ = ‭$28‬. ‭5‬ ‭So, you pay 570 less 28.5 = $541.5‬ ‭Alternatively,‬‭we‬‭know‬‭that‬‭100%‬‭of‬‭a‬‭value‬‭is‬‭equal‬‭to‬‭570.‬‭Since‬‭you‬‭get‬‭a‬‭discount‬‭of‬‭5%,‬‭you‬‭end‬‭up‬ ‭paying (100% - 5%) of the purchase price. That is:‬ ‭1 ‭9 0 5 0 ‬ ‬ * ‭570‬ = ‭$571‬. ‭5‬ ‭Just‬ ‭remember‬ ‭that‬ ‭a‬ ‭decrease‬ ‭in‬ ‭the‬ ‭price‬ ‭of‬ ‭an‬ ‭item‬ ‭(as‬ ‭compared‬ ‭to‬ ‭its‬ ‭list‬ ‭price)‬ ‭is‬ ‭termed‬ ‭as‬ ‭discount.‬ ‭Markup‬‭is‬‭when‬‭the‬‭price‬‭of‬‭an‬‭item‬‭is‬‭increased‬‭from‬‭its‬‭base‬‭price.‬‭For‬‭instance,‬‭a‬‭retailer‬‭purchases‬ ‭items‬‭from‬‭a‬‭wholesaler‬‭or‬‭manufacturer‬‭at‬‭wholesale‬‭price‬‭and‬‭then‬‭sells‬‭the‬‭same‬‭products‬‭at‬‭a‬‭higher‬ ‭price.‬ ‭The‬ ‭difference‬ ‭between‬ ‭the‬ ‭two‬ ‭prices‬ ‭is‬ ‭the‬ ‭‘markup.’‬ ‭For‬ ‭instance,‬ ‭an‬ ‭apparel‬ ‭outlet‬‭sources‬ ‭mens‬ ‭denims‬ ‭from‬ ‭the‬ ‭wholesaler‬ ‭at‬ ‭$50,‬ ‭and‬ ‭then‬ ‭adds‬‭their‬‭markup‬‭of‬‭60%‬‭before‬‭selling‬‭it‬‭to‬‭the‬ ‭customers. What is the retail price?‬ ‭Now,‬ ‭we‬ ‭can‬ ‭calculate‬ ‭the‬ ‭same‬ ‭in‬ ‭two‬ ‭ways.‬ ‭First,‬ ‭calculate‬ ‭the‬ ‭amount‬ ‭of‬ ‭markup‬ ‭and‬ ‭add‬ ‭to‬ ‭the‬ ‭purchase price. That is:‬ ‭ ‬‭‬‭ ‬ = ‭‬ ‭1 ‭6 0 0 0 ‬ ‬ * ‭50‬ = ‭$30‬ ‭Retail price = purchase price + mark up = 50 + 30 = $80‬ ‭= 75%‬

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