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------------------------------------------------ Which expression is equivalent to [tex]30\left(\frac{1}{2} x-2\right)+40\left(\frac{3}{4} y-4\right)[/tex]?

A. [tex]15x + 30y - 64[/tex]

B. [tex]15x - 30y - 220[/tex]

C. [tex]15x + 30y - 220[/tex]

D. [tex]45xy - 220[/tex]

To solve the expression [tex]$30\left(\frac{1}{2} x-2\right)+40\left(\frac{3}{4} y-4\right)$[/tex], we need to apply the distributive property to both parts of the expression, simplify, and then combine the results.

1. Distribute the 30:
- Consider the term [tex]$30\left(\frac{1}{2} x - 2\right)$[/tex].
- Distribute the 30 to each part inside the parentheses:
- [tex]$30 \times \frac{1}{2} x = 15x$[/tex]
- [tex]$30 \times -2 = -60$[/tex]
- This yields: [tex]$15x - 60$[/tex].

2. Distribute the 40:
- Consider the term [tex]$40\left(\frac{3}{4} y - 4\right)$[/tex].
- Distribute the 40 to each part inside the parentheses:
- [tex]$40 \times \frac{3}{4} y = 30y$[/tex]
- [tex]$40 \times -4 = -160$[/tex]
- This yields: [tex]$30y - 160$[/tex].

3. Combine the results:
- Now, add the expressions from the two distributed results:
- [tex]$(15x - 60) + (30y - 160)$[/tex]
- Combine like terms:
- [tex]$15x$[/tex] is already simplified.
- [tex]$30y$[/tex] is already simplified.
- Combine constants: [tex]$-60 - 160 = -220$[/tex].

So, the simplified expression is [tex]$15x + 30y - 220$[/tex].

Thus, the expression equivalent to the original is [tex]$15x + 30y - 220$[/tex].

The correct answer is: [tex]$15x + 30y - 220$[/tex].