Solving Inequalities based on Word Problems

Q.

Half the perimeter of a rectangular garden, whose length is $4$m more than its width, is $36$m .

Find the dimensions of the garden.

Q.

The perimeter of a rectangular park is $84m.$Its length is $24m.$Find its breadth.

Q.

Mary, who is sixteen years old, is four times as old as her brother.

How old will Mary be when she is twice as old as her brother?

Q. There is a group of 8 students. The number of boys is less than the numbers of girls. How many girls can there be in this group?

1. $0,1,2\text{or}3.$
2. $5,6,7\text{or}8.$
3. $4,5,6,7\text{or}8.$

Q. Twelve more than the product of a number and 2 is less than -5. Find the number.

1. $x<-\frac{17}{2}$
2. $x<-\frac{17}{2}$
3. $x>-\frac{17}{2}$
4. $x\le -\frac{17}{2}$

Q.

Among $9$ passengers, $5$ can speak Kannada, $2$ can speak both Kannada and English. What is the number of passengers who can speak only English?

Q. If Nancy, who is not yet $21$ years old, is two years older than Lily, then Lily's age will be

1. $\le 19$ years
2. $<19$ years
3. $>19$ years

Q. Jimmy has $\$29$. He went to restaurant and found out that the price of 1 pizza is $\$13$ and one burger is $\$3$. how many pizza he can afford to buy if he bought one burger?

1. 2
2. 3
3. 1
4. 4

Q. Jason got an allowance of $\$20$. He wants to save more than $\$5$ at the end of $10$ days. He spends an equal amount of money everyday. Which of the following is true?

1. Jason should spend less than $\$1.50$ daily.
2. Jason should spend more than $\$1.50$ daily.
3. Jason should spend less than or equal to $\$1.50$ daily.

Q. Rebecca's hair is 3 inches long. Her hair grows 2 inches every month. She wants her hair to be at most 9 inches. Can she go for 4 months without a haircut?

1. No. She can not wait for $4\text{months}$ without a haircut.
2. Yes. She can can go for $4\text{months}$ without a haircut.

Q. Jaffar has a square canvas with sides of 60cm length. He wants to turn it into a rectangle by reducing one pair of opposite sides, but he does not want to decrease the area by more than 10%. By how much can he reduce the length of one pair of opposite sides of the square?

1. Reduction ≤ 6 cm
2. Reduction < 9 cm
3. Reduction ≤ 7 cm
4. Reduction < 8 cm

Q. A rectangular room has a length of $x$ m and breadth of ($x+2$) m. The length of rope used to measure the length and breadth of a room is less than 24 m. Calculate the maximum length of the room if $x$ is in positive integers.

1. 4 m
2. 6 m
3. 8 m
4. 2 m

Q.

$$Write the given statement as an equation:

“If a number is added to $7$ equals $15$.”

Q. The sum of two successive integer is greater than 18. Find the smallest number which can satisfy.

1. 8
2. 9
3. 10
4. 11

Q. Imagine youself to be in a park with $\$20$. You have already spent $\$9$ on the entry fees. How much possible amount of money you can spent in the park?

1. $x\le \$11$.
2. $x\ge \$11$
3. $x<\$11$
4. $x>\$11$