The sum of three numbers is 62. The largest is 5 times the smallest, while the sum of the smallest and two times the largest is 77. Find the numbers.

Question

Equation 1:

Equation 2:

Equation 3:

The numbers are:

Show work. 

Answer 1

x is the smallest

y is the middle

z is the largest

 

 x + y + z = 62 <--- Equation #1

 

z = 5x  <--- Equation #2

 

 x + 2z = 77 <--- Equation #3

 

 

plugs the second equation into the third

x + 2(5x) = 77

x + 10x = 77

11x = 77

x=7

 

Then z is 35 because it is 5 times as large per equation #2

 

The sum is 62, so 7 + y + 35 = 62

                          y + 42 = 62

                           y = 20

 

The numbers are 7, 20, and 35

 

Answer 2

a + b + c = 62

c = 5a

a + 2c = 77

 

We can substitute the "value" of c in the 2nd equation for c in the 3rd.

 

a + 2(5a) = 77

a + 10a = 77

11a = 77

a = 7

 

c = 5(7)

c = 35

 

7 + b + 35 = 62

b + 42 = 62

b = 20

 

7, 20 and 35