Middle School Math & Grammar/ProOneSoftware-MiddleSchoolMath&Grammar-Win31.iso/math/chapter5.4b

Text File | 1993-09-25 | 6.1 KB | 317 lines

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àï5.4èSolving Percent Problems.

äè Please solve the following Percent Problems by finding
the Amount.

âèSolve the Percent Problem, "What number is 25% of 40?"

#è Aê 25è┌───¥è100 Aè=è40 ∙ 25è┌──¥è Aè=è10
#è──è=è───è│ê100 Aè=è1,000ë│
#è40ê100è│êêêê │ëThe Amount is 10.
#êê ───┘êè Aè=è1,000/100 ┘


éSIn order to solve the Percent Problem, "What number is 25% of
40?",ïyou should first identify the three parts.

êêëWhat number is 25% of 40?
êêê êè ê
êêëAmountê Rateè Base

Next, you should substitute ç three parts into the Percent
Proportion.

êëAmountêïRateêêAê 25
#êë──────è =è ────ï,êè──è=è───
êë Baseêè 100êë 40ê100

Note that the Amount, represented by the letter "A", is the unknown in
this proportion.ïNext, you should solve the proportion by cross
multiplying.
#êêë 100 ∙ Aè=è40 ∙ 25è┌¥ëAè=è10
#êêë 100 ∙ Aè=è1,000ë│
#êêêêêêï│èThe Amount is 10.
#êêêëAè=è1,000/100 ┘

 1
êêïWhat number is 35% of 200?ïFind the Amount.


ë A)ï90êëB)ï70êëC)ï85êëD)ïå

üêêêèAêï35
#êêêê ───è=è───
êêêê 200ê100
ïAmountëRate
#ï──────ï=ï────êë100 ∙ Aè=è200 ∙ 35
èBaseê100êë100 ∙ Aè=è7,000

êêêêêAè=è7,000/100

êêêêêAè=è70,èThe Amount is 70.
Ç B
 2
êê What number is 40% of 50?ïFind the Amount.


ë A)ï35êëB)ï40êëC)ï20êëD)ïå

üêêêèAêï40
#êêêê ───è=è───
êêêêï50ê100
ïAmountëRate
#ï──────ï=ï────êë100 ∙ Aè=è50 ∙ 40
èBaseê100êë100 ∙ Aè=è2,000

êêêêêAè=è2,000/100

êêêêêAè=è20,èThe Amount is 20.
Ç C
 3
êê 80% of 150 is what number?ïFind the Amount.


ë A)ï120êè B)ï110êè C)ï100êè D)ïå

üêêêèAêï80
#êêêê ───è=è───
êêêê 150ê100
ïAmountëRate
#ï──────ï=ï────êë100 ∙ Aè=è150 ∙ 80
èBaseê100êë100 ∙ Aè=è12,000

êêêêêAè=è12,000/100

êêêêêAè=è120,èThe Amount is 120.
Ç A
 4
êêï90% of 82 is what number?ïFind the Amount.


ë A)ï80êëB)ï73.8êèC)ï75êëD)ïå

üêêêèAêï90
#êêêê ───è=è───
êêêêï82ê100
ïAmountëRate
#ï──────ï=ï────êë100 ∙ Aè=è82 ∙ 90
èBaseê100êë100 ∙ Aè=è7,380

êêêêêAè=è7,380/100

êêêêêAè=è73.8,èThe Amount is 73.8.
Ç B
 5
êê What number is 75% of 180.ïFind the Amount.


ë A)ï135êè B)ï140êè C)ï145êè D)ïå

üêêêèAêï75
#êêêê ───è=è───
êêêê 180ê100
ïAmountëRate
#ï──────ï=ï────êë100 ∙ Aè=è180 ∙ 75
èBaseê100êë100 ∙ Aè=è13,500

êêêêêAè=è13,500/100

êêêêêAè=è135,è The Amount is 135.
Ç A
äïPlease solve the following Percent Problems by finding
êêthe Base.
âëSolve the Percent Problem, "52 is 65% of what number?"

#è Aê Rêï52ê 65ë┌¥ï5200è=è65∙B
#è ─è=è─── ,ë ──è=è───ë│êêë┌¥ The Base
#è Bê100êïBê100ë│ï5200/65 =ïBë│ïis 80.
#êêêêêë│êêë│
#êêë 52 ∙100è=è65∙B ─┘ë80è=èBï──┘
éSIn order to solve the Percent Problem, "52 is 65% of what
number", you should first identify the three parts.

êêë 52ïisï65%ïofïwhatïnumber?
êêë ê êè 
êêëAmountèRateê Base

Next, ç parts are substituted into the Percent Proportion.
êèAmountêïRateêê 52ê 65
#êè──────è =è ────ï,êë──è=è───
êè Baseêè 100êêïBê100

Note that the Base, represented by the letter "B", is the unknown in
this proportion.ïNext, you should solve the proportion.

#êê 100 ∙52è=è65∙Bè ┌¥ë 80è=èB
#êêè 5200è=è65∙Bè │
#êêêêêï│ë The Base is 80.
#êê 5200/65è=èBè ───┘

 6
êê 40.5 is 45% of what number?ïFind the Base.


ë A)ï75êëB)ï85êëC)ï90êëD)ïå

üêêêè40.5ê 45
#êêêêï────è=è───
êêêêè Bê 100
ïAmountëRate
#ï──────ï=ï────ê40.5 ∙ 100è=è45 ∙ B
èBaseê100êë 4050è=è45 ∙ B

êêêê4050/45ï=èB

êêêêë90è=èB,è The Base is 90.
Ç C
 7
êê 55% of what number is 38.5?ïFind the Base.


ë A)ï70êëB)ï75êëC)ï80êëD)ïå

üêêêè38.5ê 55
#êêêêï────è=è───
êêêêè Bê 100
ïAmountëRate
#ï──────ï=ï────êè38.5 ∙ 100è=è55 ∙ B
èBaseê100êë 3850è=è55 ∙ B

êêêê3850/55ï=èB

êêêêë70ï=èB,ëThe Base is 70.
Ç A
 8
êê 57 is 95% of what number?ïFind the Base.


ë A)ï55êëB)ï60êëC)ï65êëD)ïå

üêêêè 57êï95
#êêêêï────è=è───
êêêêè Bê 100
ïAmountëRate
#ï──────ï=ï────êë57 ∙ 100ï=è95 ∙ B
èBaseê100êë5700ë =è95 ∙ B

êêêê 5700/95è=èB

êêêêë 60è=èB,ëThe Base is 60.
Ç B
 9
êê 27 is 15% of what number?ïFind the Base.


ë A)ï115êè B)ï90êëC)ï180êè D)ïå

üêêêè 27êï15
#êêêêï────è=è───
êêêêè Bê 100
ïAmountëRate
#ï──────ï=ï────êë27 ∙ 100è=è15 ∙ B
èBaseê100êê2700è=è15 ∙ B

êêêê2700/15è=èB

êêêêè 180è=èB,è The Base is 180.
Ç C
 10
êêï9 is 20% of what number?ïFind the Base.


ë A)ï45êëB)ï85êëC)ï95êëD)ïå

üêêêë9êï20
#êêêêè ─è =è───
êêêêè Bê 100
ïAmountëRate
#ï──────ï=ï────êë9 ∙ 100è=è20 ∙ B
èBaseê100êêï900è=è20 ∙ B

êêêêï900/20è=èB

êêêêë 45è=èB,è The Base is 45.
Ç A
äïPlease solve the following Percent Problems by finding
êêthe Rate.

âëSolve the Percent Problem, "70 is what percent of 200?"

#è Aê Rêï70ê Rë┌¥ï7000è=è200∙R
#è ─è=è─── ,ë───è=è───è │êêë┌¥ The Rate
#è Bê100ê200ê100è │ 7000/200 =èRè │ïis 35%.
#êêêêêè │êêë│
#êêë 70 ∙100ï=ï200∙R ─┘ë35è=èRï──┘
éSIn order to solve the Percent Problem, "70 is what percent of
200?", you should first identify the three parts.

êêêï70ïisïwhat percent of 200?
êêêïê êê
êêê AmountèRateêè Base

Next, ç parts are substituted into the Percent Proportion.

êë AmountêïRateêè 70ê R
#êë ──────è =è ────ï,ê───è=è───
êêBaseêè 100êè200ê100

Note that the Rate, represented by the letter "R", is the unknown in
this proportion.ïNext, you should solve the proportion.

êë 70 ∙ 100è=è200∙R
#êêè7000è=è200∙Bè┌─¥è 35è =è R
#êêêêê │
#êë 7000/200è=èRè ───┘ëThe Rate is 35%.

 11
êêï20 is what percent of 50?ïFind the Rate.


ë A)ï45%êè B)ï35%êïC)ï40%êè D)ïå

üêêêè 20êïR
#êêêêï────è=è───
êêêêè50ê 100
ïAmountëRate
#ï──────ï=ï────êë20 ∙ 100è=è50 ∙ R
èBaseê100êë 2000è=è50 ∙ R

êêêê 2000/50 =èR

êêêêë40è=èR,è The Rate is 40%.
Ç C
 12
êêï120 is what percent of 150?ïFind the Rate.


ë A)ï80%êè B)ï85%êïC)ï90%êè D)ïå

üêêêè120êïR
#êêêêï────è=è───
êêêêï150ê 100
#ïAmountëRateêêêêêï┌─¥è80è=èR
#ï──────ï=ï────ê 120 ∙ 100è=è150 ∙ Rë │
#èBaseê100êë12000è=è150 ∙ Rë │ The Rate is 80%.
#êêêè 12000/150è=èRêï───┘
Ç A
 13
êêï73.8 is what percent of 82?ïFind the Rate.


ë A)ï80%êè B)ï85%êïC)ï90%êè D)ïå

üêêê73.8êïR
#êêêë ────è=è───ë ┌─¥è90è =è R
#ïAmountëRateêè 82ê 100ë │
#ï──────ï=ï────è 73.8 ∙ 100è=è82 ∙ Rè│è The Rate is 90%.
#èBaseê100êè7380è=è82 ∙ Rè│
#êêêè7380/82è=èRë───┘
Ç C