Let x be the larger number and y be the smaller number.
x + y = 12
The given "three times the larger number plus twice the smaller number is 33" can be written as.
3x + 2y = 33
Derive equations:
x + y = 12
x = 12 - y
y = 12 - x
.
Getting x or the larger number:
3x + 2y = 33
3x + 2(12 - x) = 33
3x + 24 - 2x = 33
3x - 2x = 33 - 24
x = 9
.
Getting y or the smaller number:
3x + 2y = 33
3(12 - y) + 2y = 33
36 - 3y + 2y = 33
-3y + 2y = 33 - 36
-y = -3
-y/-1 = -3/-1
y = 3
.
Checking:
x + y = 12
9 + 3 = 12
12 = 12
.
3x + 2y = 33
3(9) + 2(3) = 33
27 + 6 = 33
33 = 33
.
Therefore, the value of the larger and smaller number are 9 and 3, respectively.
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