8/2/2019 prob 51-60

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51. A survey of students at Frank Ohl Middle School revealed the following:

240 students are taking mathematics

195 students are taking English

215 students are taking science

150 students are taking mathematics and English

180 students are taking mathematics and science

130 students are taking English and science

100 students are taking all three subjects

How many students are included in the survey?

Understand

The problem is asking how many students are included in the

survey.

Make a Plan

Venn Diagram

Carrying the Plan

8/2/2019 prob 51-60

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52. What is the greatest number of 2-inch by 3-inch rectangular cards that can be

cut from a rectangular sheet that measures 2 feet by 3 feet?

Understand

The problem is asking the greatest number of 2-inch by 3-inch

rectangular cards that can be cut from a rectangular sheet that

measures 2 feet by 3 feet.

Make a Plan

Make use of a diagram

Carrying the Plan

1 feet = 12 inches

2 feet = 24 inches

3 feet = 36 inches

9 x 6 = 54

2 inches by 3 inches

9 x 4 = 36 inches by 3 inches

8/2/2019 prob 51-60

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53. In three bowling games, Lori scored 139, 143 and 144. What score will she

need in a fourth game in order to have an average score of 145 for all four

games?

Understand

The problem I s asking what score will Lori need in a fourth game in

order to have an average score of 145 for all four games?

Make a Plan

Making use of equation

Guess and check

Carrying the Plan

426 + x = 580

X = 580 426

X = 154

8/2/2019 prob 51-60

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54. Raymond got 85, 88 and 93 on his first three tests. What must he get on his

fourth test so that his average on the fourth test is 90 (the lowest A)?

Understand

The problem is asking for the fourth test of Raymond so that his

average on the fourth test is 90

Make a Plan

Making use of equation

Guess and check

Carrying the Plan

266 + x = 360

X = 360 266

X = 94

8/2/2019 prob 51-60

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55. If today is Tuesday, what day of the week will it be in 100 days from now?

Understand

The problem is asking the day of the week will it be in 100 days

from now I today is Tuesday.

Make a Plan

Identify the information

Working backward

Carrying the Plan

1 week = 7 days

100 / 7 = 14 .2

The remainder will be added to the given day, then

Tuesday + 2 days = Thursday

8/2/2019 prob 51-60

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56. A bag of marbles can be divided in equal shares among 2, 3, 4, 5 or 6

friends. What is the least number of marbles that the bag could contain?

Understand

The problem is asking for the least number of marbles that the bag

could contain.

Make a Plan

Getting the LCM

Carrying the Plan

2 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, to 60 = 303 3, 6, 9, 12, 15, to 60 = 204 4 to 60 = 155 5 to 60 = 126 6 to 60 = 10

8/2/2019 prob 51-60

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57. The four-digit number 3AA1 is divisible by 9. Find the value of A.

Understand

The problem is asking for the value of A.

Make a Plan

Start with the smallest # divisible by A. So that we have 9 and 18 then try it

one by one. But we have to subtract first to 4 to the # since 3 + 1 = 4

Carrying the Plan

3 + A + A + 1 = 94 + 29 = 9 429 = 9 429 5------ = ------- = A = 2.529 2

3 + A + A + 1 = 184 + 29 = 18 429 = 18 4 = 14

29 14-------- = ----------- = 7

29 2

Looking Back

Therefore, 3 + 7 + 7 + 1 = 18

18 = 18

8/2/2019 prob 51-60

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