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Lisa and Daisy work at a hair salon. The salon charges [tex]\$18[/tex] for a hair styling session with Lisa and [tex]\$12[/tex] for a session with Daisy. The income on a certain day is projected to be [tex]\$216[/tex]. This situation can be represented by the equation [tex]18x + 12y = 216[/tex], where [tex]x[/tex] is the number of Lisa's customers and [tex]y[/tex] is the number of Daisy's customers. How many customers would Lisa need to serve to attain the projected income if Daisy calls in sick that day? (Note: [tex]x \geq 0, y \geq 0[/tex], and [tex]x[/tex] and [tex]y[/tex] take only integer values.)

A. 8
B. 12
C. 18
D. 22

Sagot :

GinnyAnswer
To solve the question of how many customers Lisa would need to serve if Daisy calls in sick, we'll work through the given equation step-by-step.

The equation given is:

[tex]\[ 18x + 12y = 216 \][/tex]

Here:
- [tex]\( x \)[/tex] represents the number of customers served by Lisa.
- [tex]\( y \)[/tex] represents the number of customers served by Daisy.
- The salon's projected total income for the day is $216.

Given that Daisy is sick on this particular day and thus will not serve any customers, we can set [tex]\( y \)[/tex] to 0 in the equation. This simplifies our equation to:

[tex]\[ 18x + 12(0) = 216 \][/tex]

which reduces to:

[tex]\[ 18x = 216 \][/tex]

Next, to find the value of [tex]\( x \)[/tex], we divide both sides of the equation by 18:

[tex]\[ x = \frac{216}{18} \][/tex]

[tex]\[ x = 12 \][/tex]

Therefore, the correct answer is that Lisa would need to serve 12 customers to reach the projected income, given that Daisy is not working that day.

Thus, the correct answer is:

B. 12
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