The sum of two numbers is 21,3/4 of one of the number added to 2/3 of the other gives a sum of 15. Find the number
3/4 x + 2/3 (21-x) = 15
now solve for x
a = first number
b = second number
a + b = 21
3 / 4 a + 2 / 3 b = 15
3 a / 4 + 2 b / 3 = 15
3 ∙ 3 a / 4 ∙ 3 + 4 ∙ 2 b / 4 ∙ 3 = 15
9 a / 12 + 8 b / 12 = 15
( 9 a + 8 b ) / 12 = 15
9 a + 8 b = 12 ∙ 15 = 180
Now solve system of two equations.
a + b = 21
9 a + 8 b = 180
The solution is:
a = 12 , b = 9
Check result.
a + b = 12 + 9 = 21
3 / 4 ∙ 12 + 2 / 3 ∙ 9 = 36 / 4 + 18 / 3 = 9 + 6 = 15