Download Aim #28 - Manhasset Public Schools

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Aim #28: How do we solve word problems using a system of equations (day 2)?
Homework: Text p. 193-194 (#s 24,29,32-33) and p. 198 (#s 23,26)
Review: p. 204 (#s 20 a-b)
Do Now: To raise money, a club sold tickets to a carnival. The cost of an adult ticket
was $6.20 and a student ticket was $3.00. The number of student tickets sold was
50 more than twice the number of adult tickets sold. If the total amount of money
raised was $4,237, how many of each type of ticket was sold? Solve using a system
of equations. Define your variables!
Solve each word problem algebraically by using a system of equations.
1) Dan invested $7,000 at two different rates: 8% and 5%. If he receives $500
in annual interest from the two investments, how much did he invest at each rate?
2) A diner makes a 15% profit on its lunches and a 22% profits on its dinners. If
the diner made $2700 one day and its profit was $524, how much was made from
lunch?
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3) Joe invested $36,000, part at 5% and the rest at 7%. If his annual interest
income from the two investments was equal, how much did he invest at each rate?
4) If one is added to both the numerator and denominator of a fraction, the value
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of the fraction becomes /3 . If one is added to the denominator of the original
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fraction, the value of the fraction becomes /4 . Find the original fraction.
5) Sue has quarters and dimes such that the number of quarters is four more than
three times the number of dimes. The total value of these coins is $11.20. How
many of each coin does Sue have?
6) The difference of two numbers is 16. The larger number is five less than four
times the smaller number. Find the numbers.
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7) The Gateway Arch in St. Louis is 86 feet taller than the Washington Monument.
If the height of the Gateway Arch is 369 feet more than one-half the height of
the Washington Monument, how tall is each structure?
8) A manager at a clothing store makes $9 more per hour than a sales clerk. If
one dollar is subtracted from the manager's rate of pay, the resulting amount is
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/2 of what the sales clerk makes. Find the rate of pay for the manager and the
sales clerk.
9) The total cost of 10 gallons of regular gas and 15 gallons of premium gas is
$85.50. Premium costs $0.20 more per gallon than regular. What is the cost per
gallon of each type of gasoline?
10) George has two investments that yield a total of $185.60 in annual interest. The
amount invested at 8% is $320 less than twice the amount invested at 6%. How much
is invested at each rate?
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