Math equation

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?
Solving:
  1. “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

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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