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G ROUP 08_1112 ST. ANGELA

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P ROBLEM #1 Anna, Bryan and Philip are cousins. Anna’s age is one third of Bryan and Philip is five years older than Bryan. If the sum of the age of the cousins is 40, find the ages of each.

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S OLUTION ( PROBLEM 1): Let :X = Age of Bryan Then :X / 3 = Age of Anna X + 5 = Age of Philip X + X / 3 + X + 5=40 2X + X /3=40 - 5 ( 6X + X ) / 3=35 7X / 3=35 7X=105 X=15

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Age of Bryan = 15 years old Age of Anna = 5 years old Age of Philip = 20 years old ANSWER ( PROBLEM 1): If :X = 15 =Age of Bryan Then :X / 3 = 15/3=Age of Anna X + 5 = 15 + 5=Age of Philip And:15 + 15/3 + 15 + 5 = 40, sum of ages

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P ROBLEM #2 The sum of the digits of a two number is 7. When the digits are reversed then the number is decreased by 9. Find the number.

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S OLUTION ( PROBLEM 2): Let :Z = Ones digit Y = Tens digit X = 10Y + Z= Two digit number If10 Y + Z - 9=10 Z + Y AndZ=7 - Y Then10 Y + 7 – Y - 9=10 ( 7 – Y ) + Y 9 Y – 2=70 – 10 Y + Y 9 Y + 10 Y - Y=70 + 2 18 Y=72 Y=4

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Ones digit= 3 Tens digit= 4 Two digit number= 43 ANSWER ( PROBLEM 2): IfZ =3= Ones digit And Y + 3=7=sum of the two digits ThenY = 4=Tens digit X = 10(4) + 3= Two digit number

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P ROBLEM #3 Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per month and charge $40 per hour per student. If they have 15 students each for one hour per week. How much profit do they make together in a month? (assume 4 weeks per month)

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S OLUTION ( PROBLEM 3): Let :X= Gross profit per month Y = Net Profit per month If$400= Rent per month (monthly expenses) AndX= 15 students ($40)(4weeks) ThenY=(15) ($40) (4) – 400 =$2400 - $400 =$2000

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Gross profit per month= $ 2400 Net profit per month= $ 2000 ANSWER ( PROBLEM 1): IfX= Gross profit per month Y = Net Profit per month With a monthly expenses for a rental fee of $400 and a total of 15 students per hour per week, assuming there are 4 weeks in a month, then:

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