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Emilio owns a bakery. The number of boxes of cookies he has left on a Monday is represented by the function [tex]$x + y = 42$[/tex], where [tex]$y$[/tex] is the number of boxes of cookies remaining in the bakery and [tex][tex]$x$[/tex][/tex] is the number of hours since he opened the bakery. How many boxes did he have at the start of business on Monday? (Note: [tex]$x \geq 0, y \geq 0$[/tex], and [tex]$y$[/tex] takes only integer values.)

A. 46

B. 40

C. 42

D. 38


Sagot :

To determine how many boxes of cookies Emilio had at the start of the business on Monday, we need to consider the information given in the problem. The equation provided is [tex]\( x + y = 42 \)[/tex], where:

- [tex]\( y \)[/tex] represents the number of boxes of cookies remaining in the bakery.
- [tex]\( x \)[/tex] represents the number of hours since Emilio opened the bakery.

We are interested in finding the number of boxes of cookies Emilio had right when he opened the bakery on Monday, which corresponds to the time when [tex]\( x = 0 \)[/tex].

1. Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( x + y = 42 \)[/tex]:
[tex]\[ 0 + y = 42 \][/tex]

2. Simplify the equation:
[tex]\[ y = 42 \][/tex]

This result tells us that, at the start of the business on Monday (i.e., when [tex]\( x = 0 \)[/tex]), Emilio had [tex]\( y = 42 \)[/tex] boxes of cookies.

Therefore, the number of boxes he had at the start of the business on Monday is [tex]\(\boxed{42}\)[/tex].

The correct answer is:
C. 42