At Andy's Market, the price of a box of brand-name cereal is $1.5$ times the price of a box of generic cereal. If the price of a box of brand-name cereal is $\$3.60$ , which of the following can be used to determine $x$ , the price of a box of generic cereal in dollars? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{x}{1.5}=3.6$ $\newline$ (B) $1.5x=3.6$ $\newline$ (C) $3.6x=1.5$ $\newline$ (D) $x+1.5=3.6$

Full solution

Q. At Andy's Market, the price of a box of brand-name cereal is

1.5

times the price of a box of generic cereal. If the price of a box of brand-name cereal is

\$3.60

, which of the following can be used to determine

x

, the price of a box of generic cereal in dollars?

\newline

Choose

1

answer:

\newline

(A)

\frac{x}{1.5}=3.6

\newline

(B)

1.5x=3.6

\newline

(C)

3.6x=1.5

\newline

(D)

x+1.5=3.6

Denote Price Relationship: Let's denote the price of a box of generic cereal as $x$ dollars. According to the problem, the price of a box of brand-name cereal is $1.5$ times the price of a box of generic cereal. We can write this relationship as: $\newline$ Brand-name cereal price = $1.5 \times$ Generic cereal price
Substitute Brand-Name Price: We are given that the price of a box of brand-name cereal is $\$3.60$ . We can substitute this value into the equation from the previous step: $\newline$ $\$3.60 = 1.5 \times x$
Isolate x: To find the value of x, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by $1.5$ : $\newline$ $x = \frac{\$3.60}{1.5}$
Perform Division: Now, let's perform the division to find the value of $x$ : $x = \frac{\$3.60}{1.5}$ $x = \$2.40$
Final Calculation: The expression that represents this calculation is $\frac{x}{1.5} = 3.6$ , which corresponds to choice (A).