Transcript Ch2-Section 2.7

§ 2.7
Further Problem
Solving
Strategy for Problem Solving
General Strategy for Problem Solving
1) UNDERSTAND the problem
• Read and reread the problem
• Choose a variable to represent the unknown
• Construct a drawing, whenever possible
• Propose a solution and check
2) TRANSLATE the problem into an equation
3) SOLVE the equation
4) INTERPRET the result
• Check the proposed solution in problem
• State your conclusion
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Distance Problems: Finding Time
When the amount in the formula is distance, we refer to the
formula as the distance formula.
distance = rate · time or d = r · t
Example:
While swimming in the ocean, Missy’s sunglasses fell off her
head. If the sunglasses fall at a rate of 4 feet per second, how
long will it take for them to fall 70 feet to the sand at the
bottom?
1.) UNDERSTAND
Let t = the time it takes the glasses to fall
Continued
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Distance Problems: Finding Time
Example continued:
2.) TRANSLATE
d = rt
70 = 4t
3.) SOLVE
17.5 = t
4.) INTERPRET
It will take Missy’ sunglasses 17.5 seconds to fall to the bottom.
Check: rate · time = 4 · 17.5 = 70 
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Money Problems
interest = principal · rate · time
Example:
Jordan invested $12,500, part at 7% simple interest and part at
6% simple interest for 1 year. How much was invested at each
rate if each account earned the same interest?
1.) UNDERSTAND
Let x = the amount of money invested at 7%
Continued
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Money Problems
Example continued:
2.) TRANSLATE
principal · rate · time = interest
Account
7%
Account
6%
Account
Principal
Rate
Time
Interest
x
0.07
1
0.07x
12500 – x
0.06
1
0.06(12500 – x)
Interest from each account is the same: I.07 = I.06
0.07x = 0.06(12500 – x)
Solve the equation.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
Continued
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Money Problems
Example continued:
3.) SOLVE
0.07x = 0.06(12500 – x)
0.07x = 750 – 0.06x
0.13x = 750
x = 5769.23
4.) INTERPRET
Jordan deposited $5769.23 at 7% and 12500 – 2769.23 =
$6730.77 at 6%.
Check: Interest
7%: 5769.23(0.07) = 403.85

6%: 6730.77(0.06) = 403.85
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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