Ch 01 Number Related (3)

8/6/2019 Ch 01 Number Related (3)

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Prepared By:

Asst. Prof. Jay Kaiser S. Lariosa

MATH 7

Seminar in Problem Solving

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Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch


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Prepared by Asst. Prof. Jay Kaiser S. Lariosa

Verbal Problem


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Is a problem of mathematical nature stated in plainwords, and which would involve mathematicalcalculation of some kind before it can be solved.


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Number Related Problems

Chapter 1

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Number of Unknowns: 1


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1.Problems with One UnknownInvolves the determination of the value of a singleunknown as affected by:1.An increase/decrease by whole or fractional amountconcerning its value to form a new number.2.Taking the reciprocal or square value of the unknown.3.In association with whole unit of things or number of people.


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2.Problems with Two UnknownsSuggests the nature of greater and smaller numberbeing compared or related.1.Sum or difference of the two2.One is increased or decreased by a certain amount and givento the other3.Sum or difference of the fractional parts of the two4.Sum or product of two consecutive numbers


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3.Problems with Three or More Unknowns1.The sum of three numbers of different values2.The sum of three or more consecutive numbers3.Two or three differentiable groups of objects that differ inquantities


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Expressions and its Equivalent

Sample Expressions

i.xplus 5ii.xadded to 7iii.10 increased by kiv.tmore than 8v.5 in addition to gvi.Sum of two numbers pand 9vii.xminus 7viii.Subtract 3 from t

Algebraic Equivalent

i.x+ 5ii.7 + xiii.10 + kiv.8 + tv.g+ 5vi.p+ 9vii.x7viii.t-3

7Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch


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Sample Expressions

i.7 minus xii.cdecreased by 11iii.ndiminished by 8iv.jexceeds by 3 by 5v.wless 10vi.rless than 4vii.dlowered by 6


i.7 xii.c11iii.n8iv.j3 = 5v.w10vi.4 rvii.d-6

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Sample Expressions

i.The difference between xand 9 is 17ii.2 times a number diii.5% of number wiv.Twice a number qv.Thrice a number avi.The quotient of rand 9vii.The product of 8 and yviii.Half of a number fix.The quotient of x and 4 is 3x.The reciprocal of a number k


i.x19 = 17ii.2diii.0.05wiv.2qv.3avi.r/9vii.8yviii.fix.x/4 = 3

x.1/k



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Sample Expressions

i.Two numbers are consecutive. If one isx, the other is ii.The sum of two consecutive number isiii.The sum of two consecutive odd numberis iv.The square of a number is v.The ratio of xto kis ..


i.x+ 1ii.x+ (x+ 1)iii.x+ (x+ 2)iv.x2v.x/k



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Linear in One Unknown

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Problem Solving Proper

Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch12If thrice the number is increased by 11, the result is 35. What is the

number?Step 1: Representation of the unknownLet xbe the number

Step 2: TranslationThrice the number: 3xIncreased by 11: 3x+ 11The result is 35: 3x+ 11 = 35

Step 3: Solve for x.3x= 24x= 24/3x= 8.


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Exercise 1

Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch13If twice a number is decreased by 13, the result is 9. What is the number?

Step 1: Representation of the unknownLet xbe the number

Step 2: TranslationTwice the number: 2xDecreased by 13: 2x13The result is 9: 2x13 = 9

Step 3: Solve for x.2x= 22x= 22/2x= 11.


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Exercise 2


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Seven less than twice a number is 15. What is thenumber?


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Exercise 4

Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch16The difference between two-thirds of a number and

one-sixth of the same number is seventy-five. Whatis the number?


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Exercise 5


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Two-fifths of a certain number decreased by three-fourths is equal to seven-eights. What is the numbe?


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Exercise 6

Source: Understanding Business Statistics by John E. Hanke/Arthur G. Reitsch18If 260 tons of sugar were shipped on Thursday and

this was four times as much as was shipped onWednesday. How many tons were shipped inWednesday?


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Linear in Two Unknowns



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Exercise 7


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The sum of two numbers is 39, and their differenceis 7. What are the numbers?


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Exercise 8


21The sum of two numbers is 24. The greater numberis 10 more than the smaller. What are the numbers?


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Ch 01 Number Related (3)

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