Question

4. The difference of two integers is 9. Five times the smaller is 7 more than 3 times the larger. Find the numbers.​

Answer 1

The system of equations based on the given conditions reveals the two integers to be 17 and 26, with 17 being the smaller and 26 the larger.

Step-by-step explanation:

We are given that the difference of two integers is 9, and five times the smaller integer is 7 more than three times the larger integer. To find these integers, we set up a system of equations based on the information provided.

Let's call the smaller integer 'x' and the larger integer 'y'. The first equation comes from the known difference: y - x = 9. The second equation is based on the 'five times the smaller' and 'three times the larger' condition: 5x = 3y + 7.

To solve for x and y, we rearrange the second equation to y = (5x - 7) / 3 and substitute y in the first equation:

1. 
   
3. x = y - 9
4. 
   
6. y = (5x - 7) / 3

Substitute y from (2) into (1):

1. 
   
3. x = ((5x - 7) / 3) - 9
4. 
   
6. Multiply both sides by 3 to clear the fraction: 3x = 5x - 7 - 27
7. 
   
9. Simplify and solve for x: 3x = 5x - 34 ⇒ 34 = 2x ⇒ x = 17
10. 
    
12. Now, solve for y: y = 17 + 9 ⇒ y = 26

The two numbers are 17 and 26.

Answer 2

x = 26 and y = 17

Step-by-step explanation:

x is the larger number and y is the smaller number

the difference is 9 ⇒ x - y = 9

Five times the smaller is 7 more than 3 times the larger ⇒ 5y - 3x = 7

x - y = 9 ⇒ x = 9 + y (1)

substitute x = 9 + y in 5y - 3x = 7

5y - 3(9 + y) = 7

5y - 27 - 3y = 7

2y = 7 + 27

2y = 34

y = 34/2

y = 17

x = 9 + 17

x = 26