*Miss E. asks:*

1) the sum of 2 number is 30 the 2nd number is 2 more than thrice the 1st ..find the number?

2) the sum of 2 number is 22, 4 times the smaller is 3 more than the larger..find the number?

2) the sum of 2 number is 22, 4 times the smaller is 3 more than the larger..find the number?

**Solving:**

*“the sum of 2 number is 30 ” :*

x + y = 30

* “the 2nd number is 2 more than thrice the 1st “:*

y = 3x + 2

Substitute 3x + 2 for y in the 1st equation:

x + (3x + 2) = 30

x + 3x + 2 = 30

4x + 2 = 30

4x = 28

x + (3x + 2) = 30

x + 3x + 2 = 30

4x + 2 = 30

4x = 28

Find x:

x = 7

Substitute x = 7 in the other equation and solve for y:

y = 3x + 2

y = 3(7) + 2

y = 21 + 2

y = 23

So, the first number is 7, and the second number is 23.

* 2. “the sum of two numbers is 22” :*

x + y = 22

* “4 times the smaller is 3 more than the larger” :*

4x = y + 3

Rearrange for y to get: y = 4x – 3

Now, substitute 4x – 3 for y in the first equation:

x + (4x – 3) = 22

x + 4x – 3 = 22

5x – 3 = 22

5x = 25

x = 5

Substitute 5 for x in the second equation to get:

y = 4x – 3

y = 4(5) – 3

y = 20 – 3

y = 17

So, the smaller number is 5, and the larger number is 17.

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