Question

Tickets for a certain show were printed bearing numbers from 1 to 100. Odd number tickets were sold by receiving cents equal to thrice of the number on the ticket while even number tickets were issued by receiving cents equal to twice of the number on the ticket. How much amount was received by the issuing agency?

Answer 1

Answer:

126 dollars

Step-by-step explanation:

This is a simple question.

There are 50 even and 50 odd numbers in the first 100 numbers.

Now the total amount received (in pence) will be = 3[1+3+5+7+9...99] + 2[2,4,6,8,...100]

Applying the formula for sum of n terms of a Arithmetic Progression ($\frac{n}{2} . (a_{1}+a_{n})$ ) we have:  [2,4,6,8,...100] = $\frac{50}{2} . (2+100)$ = 2550 and  [1,3,5,7...,99] =  $\frac{50}{2} . (1+99) = 2500$

The total amount in pence becomes : 3(2500) + 2(2550) = 7500+5100 = 12600.

Converting this into dollars --> $\frac{12600}{100}$ --> 126 dollars