Answer
x = 400
Work Step by Step
1. Given: 0.04(90) + 0.12x = 0.06(460 + x)
2. Simplify and Distribute: 3.6 + 0.12x = 27.6 + 0.06x
3. Multiply both sides by 10 to the 2nd power to turn decimals into whole numbers:
100(3.6 + 0.12x) = (27.6 + 0.06x)100
360 + 12x = 2,760 + 6x
4. Add and subtract: 6x = 2,400
5. Divide: x = 400
6. Check: 0.04(90) + 0.12(400) = 0.06(460 + 400)
51.6 = 51.6, so 400 is a correct solution of the equation.
