Question

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

Answer 1

Answer: It must be (18,2) or (2,18).

Step-by-step explanation:

Since we have given that

The product of pairs of integers = 36

So, pairs must be

(1,36)

(2,18)

(3,12)

(4,9)

(6,6)

(9,4)

(12,3)

(18,2)

(36,1)

But we need the pair of integers whose sum is 20.

So, it must be (18,2) or (2,18).

Answer 2

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).