MATH SOLVE

2 months ago

Q:
# List all the pairs of integers with a product of 36. then find the pair whose sum is 20

Accepted Solution

A:

This is an excellent practice for the solution of quadratic equations.

1*36=36 => (1,36)

2*18=36 => (2,18)

3*12=36 => (3,12)

4*9=36 => (4,9)

6*6=36 => (6,6)

9*4=36 => (9,4)

12*3=36 => (12,3)

18*2=36 => (18,2)

36*1=36 => (36,1)

We can see that the sum decreases until the two factors are close (or equal) and then increases again.

The pair of integers with a sum of 20 is therefore (2,18) or (18,2).

1*36=36 => (1,36)

2*18=36 => (2,18)

3*12=36 => (3,12)

4*9=36 => (4,9)

6*6=36 => (6,6)

9*4=36 => (9,4)

12*3=36 => (12,3)

18*2=36 => (18,2)

36*1=36 => (36,1)

We can see that the sum decreases until the two factors are close (or equal) and then increases again.

The pair of integers with a sum of 20 is therefore (2,18) or (18,2).