Question

The sum of two numbers is 20 and their difference is 12.

Answer 1

Answer:

16 and 4

Step-by-step explanation:

x + y= 20

x -y =12

(add both equal #'s)

2x =32

x = 16

y=4

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Answer 2

Answer:

4 and 16

Step-by-step explanation:

First, let's find first term using sum formula:

$\displaystyle \large{S_n = \frac{1}{2} n[2a_1 + (n - 1)d]}$

We know that d or common difference is 12 and only sum of two terms so n = 2.

$\displaystyle \large{S_2 = \frac{1}{2} (2)[2a_1 + (2- 1)d]} \\ \displaystyle \large{S_2 = 2a_1 +d}$

Since sum of two numbers equal 20.

$\displaystyle \large{20 - 12= 2a_1 +12 - 12} \\ \displaystyle \large{8= 2a_1 }$

From above, subtract both sides by 12, solving for a1.

$\displaystyle \large{8= 2a_1 } \\ \displaystyle \large{4= a_1 }$

Therefore our first number is 4.

Finding next number, create an equation:-

$\displaystyle \large{4 + a_2 = 20 } \\ \displaystyle \large{4 - 4 + a_2 = 20 - 4} \\ \displaystyle \large{ a_2 = 16 }$

Another number is 16

So 4 and 16 has 12 as difference because 4+12=16 and 16-12 = 4