Md.Habibur Rahman (Ryadh): ডিসেম্বর 2012

Math Lesson-2

Be verb-------- =

Of-------------- *

Times--------- *

More than--- +

What--------- variable (x,y,z….)

Suppose, what percent of x is 3% of y? (এখানে যে varible গুলো দেওয়া আছে সেগুলো বাদলে What এর জন্য অন্য varible ধরতে হবে। অর্থাৎ (x,y) বাদে অন্যগুলো ধরতে হবে।

তাহলে দাড়ায়à p%x=3%y.

1. Carla has 2 more than 3 times the number of cassette tapes that Jules has. If C represents the number of Carla’s tapes and if J represents the number of Jules’s tape, which of the following is a correct expression relating C and J?

Here, Carla = C

Jules = J

C=2+3.J

2. In a weight-lifting competition, the total weight of Joe’s two lifts was 750 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?

Suppose, First lift = x

Second lift = y

X+Y=750---- (1)

2x=300+Y---- (2)

From (1) we get, Y=750-X

2x=300+750-X

3x=1050

X=1050/3

X=350

So the weight of first lift=350 pound.

3. The total fare for 2 adults and 3 children on an excursion boat is $14.00. If each child’s fare is one half of each adult’s fare, what is the adult fare?

One half = ½

One & half = 1 ½ .

Here, 1 adult’s fare = 2 child’s fare. (1 child’s fare = ½ adult’s fare).

So, 2 adult’s fare = (2*2) child’s fare.

So, (4+3) =7 Children fare = 14

1 Children fare = 14/7 = 2

& 3 children’s fare = (3*2) = 6

So, 2 adult’s fare = (14-6) = 8.

Each adult’s fare = 8/2 = 4.

4. A postal clerk sold 75 stamps for a total of $10.85. Some of the stamps were 13-cent stamps and rest was 15-cent stamps. How many of the stamps were 13-cent stamps?

Tips:- এ ধরনের আংকে যেটা বের করতে বলবে প্রথমে তা বাদ দিয়ে অন্যটা নিয়ে চিন্তা করতে হবে। যেমন এখানে প্রথমে 13-cent বাদ দিয়ে 15-cent নিয়ে চিন্তা করব। তা হলে সবগুলো যদি 15-cent এর হয় মোট পরিমান দাড়ায়= (15*75) = 1125. But total is given = $10.85 or 1058-cent.

So, (1125-1085)/ (15-cent – 13-cent) = 40/2 = 20.

So, 13-cent stamps were = 20

And 15-cent stamps were = (75-20) = 55. (Recommended)

Other Process:-

Suppose, Number of 13-cent stamps = x

& Number of 15-cent stamps = 75-x

So, 13x + 15 (75-x) =1085

ð 13x+1125-15x=1085

ð -2x= -40

ð X = 20

So, 13-cent stamps were = 20

And 15-cent stamps were = (75-20) = 55.

5. If the cost of x gallons of unleaded gasoline priced at $1.24 per gallon equals the cost of x+2 gallons of regular gasoline price at $1.16 per gallon, then x = ?

So, 1.24x = 1.16 (x+2)

ð 1.24x = 1.16x+2.32

ð 1.24x-1.16x = 2.32

ð .8x=2.32

ð X = 2.32/.8

ð X = 29

6. If Jack had twice the amount of money that he has, he would have exactly the amount necessary to buy 3 hamburgers at $0.96 apiece and 2 milk shakes at $1.28 apiece. How much money does Jack have?

Amount require to buy 3 hamburgers = (3*0.96) = 2.88

Amount require to buy 2 milk shakes = (2*1.28) = 2.56

Total amount require = 5.44

So, Jack have = (5.44/2) = 2.72.

7. The number p is 4 more than 3 times the number r. The sum of p and r is 10. Which of the following pairs of equations could be used to find the values of p and r?

P= 4+3r------- (1)

P + r = 10----- (2)

8. Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill how old will Jack be in 5 years?

Tips: - এ ধরনের অংকে সর্বপ্রথম বর্তমান বয়স বের করতে হবে।

Suppose, Present age of Jack =X+14

Present age of Bill = X

After 10 years Jack will be---(X+14+10) =(X+24)

After 10 years Bill will be----(X+10)

J=2B

ð X+24 = 2(X+10)

ð X+24=2X+20

ð X=4

So, present age of Jack = (4+14) =18.

So, after 5 years jack will be = (18+5) =23.

9. The ratio between the ages of A and B at present is 2:3. Five years hence the ratio of their ages will be 3:4. What is the present age of A?

Suppose, Present age of A =2x

Present age of B =3x

So, 5 years hence the age of A=2x+5

5 years hence the age of B=3x+5

ð 4(2x+5)=3(3x+5)

ð 8x+20=9x+15

ð X=5

So, the present age of A = (2*5) =10.

10. Three years ago the average age of A and B was 18 years. With C joining them, the average becomes 22 years. How old is C now?

After joining C,

average will be,

ð A+B+C = 66

ð 42+C = 66

ð C = 66-42

ð C = 24

3 year ago the age of A = A-3

3 year ago the age of B = B-3

So,

=18

ð (A-3)+(B-3)=36

ð A+B = 42-----(1)

11. The ratio of the father’s age to the son’s age is 4:1. The product of their ages is 196. The ratio of their ages after 5 years will be:

Suppose, Father age = 4x

Son’s age = x

So, 4x.x=196

ð 4

=196

=196/4

ð x =

ð x = 7

So, Father’s age= (4*7) =28

Son’s age = 7

So, after 5 years the ratio will be à (28+5):(7+5) = 33:12 = 11:4.

12. If 2<x<5 and 3<y<6, which of the following describes all of the possible values of x+y?

2 < x < 5

3 < y < 6

5<x+y<11

So, 5<x+y<11

13. If 0<x<4 and y<12, which of the following CANNOT be the value of xy?

Though value of x<4 & y<12, so, 4*12=48, cannot be the value of xy.

14. If w>x, y<z and x>z, then which of the following must be true?

w>x

y<z

x>z

So, w>x>z>y. or,y<z<x<w.

15. If ab>0 and a<0, which of the following is negative?

Though a<0, so the value of a is negative. We know (-,-) =+ & (-,+)= -. So, if we want to get positive value, the value of b must be negative. But here mentioned that which of the following is negative? So, ans. is àb

16. If it is true that x >-2 and x<7, which of the following must be true?