Solve the iem 7 Three times a number decreased by fifteen is

Solve the iem. 7. Three times a number decreased by fifteen is equal to the quotient of the numbers twenty-one and seven. What is the number? 8. You got elected to the Council by winning with 132 votes more than you opponent. If 510 people voted, how many votes did you get? Congrats on your election! 9. You bought a textbook and a calculator for the math class. You paid three times as much for the textbook as you did for the calculator. If your total purchase came to $164, how much did you spend on each item? 0 2 3 3

Solution

7)

Let the required number be \'x\'

Given that 3 times of number is decreased by 15. i.e.,3x-15

This will be equal to quotient of 21 and 7

Quotient of 21 and 7 is 3

So, 3x-15=3

3x=3+15

3x=18

x=6

Therefore, the required number is \'6\'

8)

Given that there are total of 510 voters.

Let I got \'X\' votes then given that my opponent got 132 votes lessthan my votes i.e., My opponent got x-132 votes.

Total votes are Votes for me + Votes for my opponent =510

X+X-132=510

2X-132=510

2X=510+132

2X=642

X=321

Therefore,I got 321 votes.

9)

Given that I bought calculator and a textbook.

Cost of textbook is 3 times the cost of calculator

Let cost of calculator is \'$X\', then

cost of textbook is \'$3X\'

Total cost of calculator and textbook is $164

i.e., X+3X=164

4X=164

X=41

3X=3*41=123

Therefore, cost of calculator= $X= $41

cost of textbook= $3X= $123