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Section 9-6Problem Solving Skills: Work Backwards
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Essential Question• How do you solve real-world applications by working backward?• Where you’ll see this: • Part-time jobs, ﬁnance, travel
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus?
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 3rd stop: 2nd stop: 1st stop:
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: 2nd stop: 1st stop:
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: Same as third stop 2nd stop: 1st stop:
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: 5 got on Same as third stop 2nd stop: 1st stop:
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: 5 got on Same as third stop 1/2 the 2nd stop 2nd stop: 1st stop:
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: 5 got on Same as third stop 1/2 the 2nd stop 2nd stop: 10 got on 1st stop:
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: 5 got on Same as third stop 1/2 the 2nd stop 2nd stop: 10 got on 1st stop: 1/2 the 1st stop
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: 5 got on Same as third stop 1/2 the 2nd stop 2nd stop: 10 got on 1st stop: 20 got on 1/2 the 1st stop
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: 5 got on Same as third stop 1/2 the 2nd stop 2nd stop: 10 got on 1st stop: 20 got on 1/2 the 1st stop 5+5+10+20
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: 5 got on Same as third stop 1/2 the 2nd stop 2nd stop: 10 got on 1st stop: 20 got on 1/2 the 1st stop 5+5+10+20 =40
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Example 1 After four stops, every seat in a school bus was taken. Half as many students got on at the second stop as atthe ﬁrst stop, and half as many got on at the third stop as at the second stop. At the fourth stop, ﬁve students got on, the same number as at the third stop. How many passenger seats were there on that bus? 4th stop: 5 got on 3rd stop: 5 got on Same as third stop 1/2 the 2nd stop 2nd stop: 10 got on 1st stop: 20 got on 1/2 the 1st stop 5+5+10+20 =40 seats
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Example 2Matt Mitarnowski has $14 in his pocket now. Duringthe day, he spent $27.45 on fez hats, $8.62 on bubble gum, and $6 on toys from vending machines. How much money did he start out with?
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Example 2Matt Mitarnowski has $14 in his pocket now. Duringthe day, he spent $27.45 on fez hats, $8.62 on bubble gum, and $6 on toys from vending machines. How much money did he start out with? Has $14, spent $27.45, $8.62, $6
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Example 2Matt Mitarnowski has $14 in his pocket now. Duringthe day, he spent $27.45 on fez hats, $8.62 on bubble gum, and $6 on toys from vending machines. How much money did he start out with? Has $14, spent $27.45, $8.62, $6 14+27.45+8.62+6
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Example 2Matt Mitarnowski has $14 in his pocket now. Duringthe day, he spent $27.45 on fez hats, $8.62 on bubble gum, and $6 on toys from vending machines. How much money did he start out with? Has $14, spent $27.45, $8.62, $6 14+27.45+8.62+6 =$56.07
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Example 3 After Shecky planted 42 bubble gum trees, 32 cottoncandy bushes, and 25 graphing calculator plants in his garden, he had 185 plants in all. How many plants were in the garden before he added to them?
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Example 3 After Shecky planted 42 bubble gum trees, 32 cottoncandy bushes, and 25 graphing calculator plants in his garden, he had 185 plants in all. How many plants were in the garden before he added to them? In the end, he has 185 plants
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Example 3 After Shecky planted 42 bubble gum trees, 32 cottoncandy bushes, and 25 graphing calculator plants in his garden, he had 185 plants in all. How many plants were in the garden before he added to them? In the end, he has 185 plants He just planted 42, 32, and 25 plants
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Example 3 After Shecky planted 42 bubble gum trees, 32 cottoncandy bushes, and 25 graphing calculator plants in his garden, he had 185 plants in all. How many plants were in the garden before he added to them? In the end, he has 185 plants He just planted 42, 32, and 25 plants 185-42-32-25
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Example 3 After Shecky planted 42 bubble gum trees, 32 cottoncandy bushes, and 25 graphing calculator plants in his garden, he had 185 plants in all. How many plants were in the garden before he added to them? In the end, he has 185 plants He just planted 42, 32, and 25 plants 185-42-32-25 = 86 plants
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Problem Set p. 400 #1-17“Live up to the best that is in you: Live noble lives, as you all may, in whatever condition you may ﬁnd yourselves.” - Henry W. Longfellow
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