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10 rubber stamps cost
$10.30.
Which equation would help determine the cost of 2 rubber stamps?
Choose 1 answer:
(A)
(2)/(x)=($10.30)/(10)
(B)
(x)/(2)=(10)/($10.30)
(c)
(2)/(10)=($10.30)/(x)
(D)
(2)/($10.30)=(x)/( 10)
(E) None of the above

$10$ rubber stamps cost $\$ 10.30$ . $\newline$ Which equation would help determine the cost of $2$ rubber stamps? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{2}{x}=\frac{\$ 10.30}{10}$ $\newline$ (B) $\frac{x}{2}=\frac{10}{\$ 10.30}$ $\newline$ (C) $\frac{2}{10}=\frac{\$ 10.30}{x}$ $\newline$ (D) $\frac{2}{\$ 10.30}=\frac{x}{10}$ $\newline$ (E) None of the above

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Compare linear and exponential growth

Full solution

Q.

10

rubber stamps cost

\$ 10.30

.

\newline

Which equation would help determine the cost of

2

rubber stamps?

\newline

Choose

1

answer:

\newline

(A)

\frac{2}{x}=\frac{\$ 10.30}{10}

\newline

(B)

\frac{x}{2}=\frac{10}{\$ 10.30}

\newline

(C)

\frac{2}{10}=\frac{\$ 10.30}{x}

\newline

(D)

\frac{2}{\$ 10.30}=\frac{x}{10}

\newline

(E) None of the above

Denote Cost as $x$ : Let's denote the cost of one rubber stamp as $x$ dollars. We know that $10$ rubber stamps cost $\$10.30$ . We want to find an equation that relates the cost of $2$ rubber stamps to the cost of $10$ rubber stamps. The direct proportionality between the number of stamps and the total cost suggests that we can set up a ratio comparing the cost of $2$ stamps to the cost of $10$ stamps.
Set Up Proportion: We can write the proportion as $(\text{cost of } 2 \text{ stamps})/(\text{cost of } 10 \text{ stamps}) = (\text{number of stamps for } 2)/(\text{number of stamps for } 10)$ . This simplifies to $(2x)/(10.30) = 2/10$ . We want to solve for $x$ , the cost of $2$ stamps.
Cross-Multiply to Solve: To solve for $x$ , we can cross-multiply to get $2 \times 10.30 = 2x \times 10$ . This simplifies to $20.60 = 20x$ . Now we can divide both sides by $20$ to find the value of $x$ .
Calculate Cost of $2$ Stamps: Dividing both sides of the equation $20.60 = 20x$ by $20$ gives us $x = \frac{20.60}{20}$ . This simplifies to $x = 1.03$ . Therefore, the cost of $2$ rubber stamps is $2 \times 1.03 = \$(2.06)$ .
Match Proportion to Choices: Now we need to match our proportion to the given answer choices. The correct proportion that we used is $(2x)/(10.30) = 2/10$ , which simplifies to $x = 1.03$ , the cost of $2$ stamps. This proportion is represented by choice (C) $(2)/(10)=(\$(10.30))/(x)$ .

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