Question

Fifteen postcards cost Rs. $2.25$. What will be the cost of $36$ postcards? How many postcards can we buy in Rs. $45$

Answer 1

Hint: Here we will use the concepts of cross multiplication and using the method of proportion to get the values. Here we are given the cost of many and we have to find the cost of the other many numbers that will use the multiplication and the division.

Complete step-by-step answer:
Here we are given that-
15 postcards cost = 2.25 Rs.
$\therefore 36$ postcards cost $ = ?$
Here, cross multiple where the left side of one side is multiplied with the opposite side of the other equation and vice-versa.
$ = \dfrac{{36 \times 2.25}}{{15}}$
Remove the decimal point and place $100$ below it since we have two digits after the decimal point.
$ = \dfrac{{36 \times 225}}{{15 \times 100}}$
Find factors of the term on the numerator –
$ = \dfrac{{36 \times 15 \times 15}}{{15 \times 100}}$
Common factors from the numerator and the denominator cancel each other.
$ = \dfrac{{36 \times 15}}{{100}}$
Find the product of the terms on the numerator –
$ = \dfrac{{540}}{{100}}$
Simplify the above expression placing the decimal point based on the numerator –
$ = 5.40$Rs.
Hence, the cost of $36$ postcards will be Rs. $5.40$ …. (A)
Now, second case,
If $2.25$ Rs can purchase $ = 15$ postcards
$\therefore Rs.45 = ?$ postcards
Apply, cross- multiplication –
$ = \dfrac{{45 \times 15}}{{2.25}}$
Simplify the above expression by removing decimal point-
$ = \dfrac{{45 \times 15}}{{\dfrac{{225}}{{100}}}}$
Denominator’s denominator goes to the numerator –
$ = \dfrac{{45 \times 15 \times 100}}{{225}}$
Find factors of the above expression –
$ = \dfrac{{15 \times 3 \times 15 \times 100}}{{15 \times 15}}$
Common factors from the numerator and the denominator cancel each other and therefore remove and from the numerator and the denominator.
$ = 3 \times 100$
Simplify finding the product of the terms in the above expression –
$ = 300$ postcards
Hence, in Rs. $45$we can buy .$300$.postcards. …. (B)

Note: Always remember that the common factors from the numerator and the denominator cancels each other. Be good in finding the factors of the term. Factor are the numbers which when multiplied together to get the original number. Remember the multiples at least till twenty.