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Rachel can buy licorice sticks for [tex]\$0.75[/tex] and cherry candies for [tex]\$0.50[/tex] and has a budget of [tex]\$25[/tex]. If her expenses are represented by the equation [tex]0.75x + 0.5y = 25[/tex], where [tex]x[/tex] is the number of licorice sticks and [tex]y[/tex] is the number of cherry candies, how many cherry candies can she buy if she wishes to spend the entire [tex]\$25[/tex] on cherry candies? (Note: [tex]x \geq 0[/tex], [tex]y \geq 0[/tex], and [tex]x[/tex] and [tex]y[/tex] take only integer values.)

A. 20
B. 25
C. 50
D. 100

Sagot :

GinnyAnswer
To determine how many cherry candies Rachel can buy if she wishes to spend the entire [tex]$25 on cherry candies, we need to set the number of licorice sticks \( x \) to zero in the given equation and solve for \( y \). The given equation representing her expenses is: \[ 0.75x + 0.5y = 25 \] 1. Set \( x = 0 \) since she only wants to buy cherry candies: \[ 0.75(0) + 0.5y = 25 \] 2. Simplify the equation: \[ 0 + 0.5y = 25 \] \[ 0.5y = 25 \] 3. Solve for \( y \): \[ y = \frac{25}{0.5} \] \[ y = 50 \] So, the number of cherry candies Rachel can buy if she wishes to spend the entire $[/tex]25 on them is:
[tex]\[ \boxed{50} \][/tex]
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