find sm number

Question

if the sum of two numbers is 80 and the difference is 54 find smaller number x+y=80

x-y=54

Answer 1

If the sum of two numbers is 80 and the difference is 54 find smaller number x+y=80
x-y=54

 

1.  solve for x.

2.  x + y = 80

3. x = 80 - y

4. Substitute the x value (80 - y) into the next statement, x - y = 54

5.  (80 - y) - y = 54

6.  80 - 2y = 54

7.  Solve for y.

8.  80 - 54 - 2y + 2y = 54 - 54 + 2y

9.  26 = 2y

10.  Divide both sides by 2

11.  26/ 2  =  2y / 2

12.  13 = y

13.  If x + y = 80, plug in 13 for y to find x.

14.  x + 13 = 80

15.  x + 13 - 13 = 80 - 13

16.  x = 67

17.  Check:  x = 67, y = 13

x + y = 80 =   67 + 13 = 80; 

x - y = 54 =    67 - 13 = 54

 

Small number= 13

 

Answer 2

Hi Lila;

 

Let's subtract the two equations from each other...

x+y=80

-(x-y)=54

0+2y=26

2y=26

y=13

 

Let's add the two equations together...

x+y=80

x-y=54

2x+0=134

2x=134

x=67

 

y=13 is the smaller number.

Answer 3

Since you cannot find the values of two unknowns at the same time, put x in terms of y. For example, since x+y=80, then you know that x=80-y, and you can now substitute the 80-y into your second equation. Now solve for y and then you'll be able to solve for x.