Question

Solve the following problems on numbers. Show your solution.

1. The sum of the two numbers is 91. The smaller number is 17 less than the larger number. What are the numbers? (2 points)

2. Twice the sum of a number and 8 is 24. Find the number. (1 point)

3. Find three consecutive integers such that the sum of the first and the third is 8 more than the second number. (3 points)

Answer 1

Q1. The larger number is 54 and the smaller number is 37.

Q2. The number is 4.

Q3. The three numbers are 7, 8 and 9.

Explanation:

Q1.

Let the larger number be x and the smaller number be y.

x+y= 91 (1)

x-y= 17 (2)

From (2) :

x= y+17 (3)

sub (3) into (1) :

y+17+y= 91

2y= 74

y= 37 (4)

sub (4) into (3) :

x= 37+17

= 54

Q2.

Let the unknown number be x.

2x+16= 24

2x= 8

x= 4

Q3.

Let the smallest number be x.

2nd no. : x+1

3rd no. : x+2

x+(x+2)= (x+1)+8

2x+2= x+9

x= 7

x+1= 8

x+2= 9