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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]$45 xy-220$[/tex]
B. [tex]$15x-30y-220$[/tex]
C. [tex]$15x+30y-220$[/tex]
D. [tex]$15x+30y-64$[/tex]

Answer :

To solve the expression [tex]\(30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right)\)[/tex], let's break it down step by step.

1. Distribute the constants in each part of the expression:

- For the first part, [tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex]:

- Distribute 30 into the expression:
[tex]\[
30 \times \frac{1}{2} x = 15x
\][/tex]
[tex]\[
30 \times 2 = 60
\][/tex]
- So, [tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex] becomes [tex]\(15x - 60\)[/tex].

- For the second part, [tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex]:

- Distribute 40 into the expression:
[tex]\[
40 \times \frac{3}{4} y = 30y
\][/tex]
[tex]\[
40 \times 4 = 160
\][/tex]
- So, [tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex] becomes [tex]\(30y - 160\)[/tex].

2. Combine the results from each part:

After distributing, combine the expressions:
[tex]\[
15x - 60 + 30y - 160
\][/tex]

3. Simplify the combined expression:

Combine like terms:
[tex]\[
15x + 30y - 220
\][/tex]

The expression is simplified to [tex]\(15x + 30y - 220\)[/tex]. This matches one of the given options:

- [tex]\( 15x + 30y - 220 \)[/tex]

Therefore, the expression is equivalent to this option.

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