Wednesday, January 11, 2012
Obj: Matching Expressions and Equations to Situations
Tamyra's soccer team scored a total of 40 goals this year. They scored 15 more goals this year than they did last year. She wrote the following equation to represent this. What did she do wrong?
g ­ 15 = 40
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Five Steps for Problem Solving
1. Familiarize yourself with the problem situation.
2. Translate the problem to an expression.
3. Solve the expression.
4. Check the answer in the original problem.
5. State the answer to the problem clearly. 2
Example 1:
Seth is 12 years old. Jessica is 9 more than twice Seth's age. How old is Jessica?
Familiarize. We want to find Jessica's age given that she is 9 more than twice Seth's age.
9 more than twice Seth's age = 2 times Seth's age plus 9.
Translate. Let S represent Seth's age. Then
2 times Seth's age plus 9 = 2 × S + 9 = 2 × 12 + 9.
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Example 2:
Josh wants to buy a bicycle priced at $127.95, but Josh only has $86.42. How much more money does Josh need to be able to buy the bicycle?
Familiarize. Josh needs $127.95, but he only has $86.42. We need to find the difference.
Translate. $127.95 ­ $86.42 = Amount Needed
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Example 3:
Bernice swam 1,750 m yesterday at the school's swimming pool. One lap at the pool is 350 m. Bernice wants to swim 2,800 m today. How many laps around the pool should Bernice swim today? Familiarize. Bernice wants to swim 2,800 m and each lap is 350 m. We need to find how many laps equal 2800 m.
Translate. Let L equal one lap around the pool. Then we want to solve 350L = 2,800
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1.) A chef ordered 10 more pounds of steak this week than he did last week. Let x stand for the number of pounds of steak he ordered last week. What is an expression that represents how many pounds of steak he ordered this week?
x + 10
10x
x ­ 10
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2.) Ajay has half as many coins in his coin collection as Shabana has in her collection. If s stands for the number of coins in Shabana's collection, write an expression that represents the number of coins in Ajay's collection.
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3.) The price of a book is 3 dollars less at the discount bookstore than at the regular bookstore. If p stands for the price of a book at the regular bookstore, write an expression that represents the price of that same book at the discount bookstore.
p­3
3­p
p+3
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4.) A store sells new and used DVDs. Buying a DVD new costs 4 times as much as buying the same DVD used. If u stands for the cost of a used DVD, write an expression that represents the cost of a new DVD.
4 + u
4 x u
u ­ 4
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5.) The length of Margo's living room is twice the length of her bedroom. If the length of the living room is 8 meters, write an equation that could be used to represent b, the length of her bedroom in meters.
2 + b = 8
b ­ 2 = 8
2 x b = 8
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6.) A deli charges $4 per pound for turkey. The cost of p pounds of turkey is $16. Write an equation that could represent this situation.
16 = 4 + p
16 = 4 x p
16 = 4 ­ p
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7.)
Jodie says that if she were 5 inches shorter, she would be 60 inches tall. Write an equation that can be used to represent Jodie's current height in inches, h.
h + 5 = 60
h x 5 = 60
h ­ 5 = 60
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8.) Yesterday, Norma rode her bike for 5 more miles than Marlena did. If Norma rode her bike for a total of 12 miles, what equation can be used to represent m, the number of miles Marlena rode her bike?
5 + m = 12
5 x m = 12
5 + 12 = m
12 x m = 5
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Homework
Worksheet
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