In this page word problem solution3 we are going to
see solution for first word problem of the worksheet cross multiplication
method.

Formulate the following problems as a pair of equations,and hence find their solutions:

(iii) A two digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number.

**Solution:**

Let "x y" be the required two digit number

Here x is in the ten's digit place and y is in unit place. To form the first equation we have to consider this particular from the question that is a two digit number(xy) is seven times the sum of its digits

x y = 7 (x + y)

Now we have to write the two digit number (xy) in expanded form

10 x + 1 y = 7 x + 7 y

10 x - 7 x + 1 y - 7 y = 0

3 x - 6 y = 0 ------ (1)

To form the second equation we have to consider this particular from the question that is The number formed by reversing the digits is 18 less than the given number.

y x = x y - 18

10 y + 1 x = 10 x + 1 y - 18

10 x - 1 x + 1 y - 10 y = 18

9 x - 9 y = 18

Divide the whole equation by 2 => x - y = 2 ----- (2)

Multiply the second equation by 6 we get

6 x – 6 y = 12

3 x - 6 y = 0

6 x – 6 y = 12

(-) (+) (-)

------------------

- 3 x = -12

x = (-12)/(-3)

x = 4

Now we have to apply the value of x in the first or second equation to get the value of y.

Substitute x = 4 in the first equation we get

3 x - 6 y = 0

3(4) - 6 y = 0

12 - 6 y = 0

-6 y = - 12

y = (-12)/(-6)

y = 2

x – y = 2

4 - 2 = 2

2 = 2

word problem solution3 word problem solution3 word problem solution3

- Elimination method
- Elimination method worksheet
- Cross Multiplication Method
- Word problems on age
- Word problems on digits
- Word problems on numbers
- Word problems on percents
- Mixed word problems

(i) One number is greater than thrice
the other number by 2. If 4times the smaller number exceeds the greater by 5,
find the numbers. Solution

(ii) The ratio of income of two persons is 9:7 and the ratio of their expenditure is 4:3.If each of them manages to save $2000 per month, find their monthly income. Solution

(iv) Three chairs and two tables cost $700 and five chairs and three tables cost $1100.What is the total cost of 2 chairs and 3 tables. Solution

(v) In a rectangle,if the length is increased and breadth is reduced each by 2 cm then the area is reduced by 28 cm ². If the length is reduced by 1 cm and the breadth is increased by 2 cm,then the area increases by 33cm². Find the area of the rectangle. Solution

(vi) A train traveled a certain distance at a uniform speed. If the train had been 6 km/hr faster,it would have taken 4 hours less than the scheduled time. If the train were slower by 6km/hr, then it would have taken 6 hours more than the scheduled time. Find the distance covered by the train. Solution