Representing Linear Equations for a Word Problem

Q. Reversing the digits of a two digit number the number obtained is 9 less than 3 times the original number if the difference of these two numbers is 45 find the original number.

Q.

Sum of the two digits of a number is $9$.

When we interchange the digits the new number is $27$ greater than the earlier number.

Find the number.

Q.

Solve by substitution method :

$x+2y=-1and2x-3y=12$

Q. A natural number, when increased by 12, equals 160 times its reciprocal find the number.

Q. When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3. Find the fraction.

Q.

In a competitive examination, one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

Q.

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator.If the numerator and denominator are increased by 3, they are in the ratio 2:3.Determine the fraction.

Q.

There are two positive integers $X$ & $Y.$ When $X$ is divided by $237,$ the remainder is $192.$ When Y is divided by $117$ the quotient is the same but the remainder is $108.$ Find the remainder when the sum of $X$ & $Y$ is divided by $118.$

Q.

A two digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number the digits are reversed. Find the numbers

Q. One says, "Give me a hundred, friend! I shall then become twice as rich as you." The other replies, "If you give me ten, I shall be six times as rich as you." Tell me what is the amount of their respective capital?

Q. seven times a two digit number is equal to four times the number obtained by reversing the order of its digits.If the difference of the digits is 3 find the number

Q.

Find two numbers such that the sum of thrice the first and the second is 142, and four times the first exceeds the second by 138.

Q.

If 45 is subtracted from twice the greater of two numbers, it results in the other number.If 21 is subtracted from twice the smaller number, it results in the greater number.Find the numbers.

Q.

Two numbers are in the ratio 2 : 3. If 9 is added to each, they will be in the ratio 3 : 4. Find the numbers.

1. The numbers are 18, 27

2. The numbers are 9, 12

3. The numbers are 12, 16

4. The numbers are 15, 20

Q. A number consists of two digits whose sum is 10. If 18 is subtracted from the number, its
digits are reversed. Find the number.

Q.

Solve the following pair of linear equations by the substitution method:

$$\begin{gathered} x+y=14 \\ x-y=4 \end{gathered}$$

Q.

In the morning a farm worker packed $3$ pints of strawberries every $4\mathrm{minutes}$, in the afternoon she packed $2$ pints of strawberries every $3\mathrm{minutes}$. What was the difference between her morning and afternoon packing rates, in pints per $\mathrm{hour}$?

Q. A jeweller has bars of 18-carat gold and 12-carat gold. How much of each must be melted together to obtain a
bar of 16-carat gold, weighing 120 g?

Q.

Question 91

Solve the following:

After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.

Q.

5 chairs and 4 tables together cost Rs.5600, while 4 chairs and 3 tables together cost Rs.4340.Find the cost of a chair and that of a table.

Q. A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.

Q.

Two men buy apples and oranges. One person buys 5 apples and 2 oranges for ₹20. Another person buys 3 apples and 5 oranges for ₹ 31. Find the algebraic expression representing the above condition.

1. $5x+2y=20;3x+5y=31$

2. $2x+5y=30;5x+3y=31$

3. $5x+2y=30;5x+3y=31$

4. $2x+5y=20;3x+5y=31$

Q.

Question 81

The normal body temperature is ${98.6}^{\circ }$ F. When Savitri was ill, her temperature rose to ${103.1}^{\circ }$ F. How many degrees above normal was that?

Q.

The difference between a two digit number and the number obtained by the interchanging the digits is 27. What is the difference between the two digits of the number?

Q.

If speed of boat in still water is x km/h and speed of stream is y $\frac{km}{h}$ .

S1 : upstream speed of boat is (x-y) $\frac{km}{h}$

S2 : downstream speed is (x+y) $\frac{km}{h}$

1. S1 and S2 are true

2. S1 is true and S2 is false

3. S1 is false and S2 is true

4. S1 and S2 are both false

Q.

Seven years ago, Varun's age was 5 times the square of swatis age. Three years hence swatis age will be two fifth of Varun's age. Find their present ages if Varun's present age is x and swatis present age is y.

Q. The sum of the digits of a three-digit number is 11.If the digits are reversed, the new number is 46 more than five times the former number.If the hundreds digit plus twice the tens digit is equal to the units digit, then find the three equations using which we can find the original three-digit number.

1. 4x+7y+9z=135
2. x +y +z=11
   
3. 499x+40y-95z = -46
4. x+2y-z=0

Q.

How do you solve for $y$ in $3x+2y=12$?

Q. Half the perimeter of a rectangular garden, whose length is 8 m more than its width, is 40 m. Find the dimensions of the garden.

1. Length = 20m, Breadth = 18m
2. Length = 24m, Breadth = 16m
3. Length = 24m, Breadth = 20m
4. Length = 40m, Breadth = 36m

Q.

Solve for x and y.

x+y=a+b

ax-by=a^2-b^2

Solve by substitution and elimination method.