One Pound Of Grapes Costs $ 1.55 \$1.55 $1.55 . Which Equation Correctly Shows A Pair Of Equivalent Ratios That Can Be Used To Find The Cost Of 3.5 Pounds Of Grapes?A. 1.55 1 = X 3.5 \frac{1.55}{1}=\frac{x}{3.5} 1 1.55 ​ = 3.5 X ​ B. 1.55 1 = 3.5 X \frac{1.55}{1}=\frac{3.5}{x} 1 1.55 ​ = X 3.5 ​ C.

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Understanding Equivalent Ratios

When dealing with ratios, it's essential to understand that equivalent ratios have the same value, but the numbers may be different. In this case, we're given the cost of one pound of grapes, which is $\$1.55$. We need to find the cost of 3.5 pounds of grapes using a pair of equivalent ratios.

What are Equivalent Ratios?

Equivalent ratios are ratios that have the same value, but the numbers may be different. For example, $\frac{2}{4}$ and $\frac{1}{2}$ are equivalent ratios because they have the same value, even though the numbers are different.

Setting Up the Equation

To find the cost of 3.5 pounds of grapes, we need to set up a pair of equivalent ratios. The first ratio is the cost of one pound of grapes, which is $\$1.55$. The second ratio is the cost of 3.5 pounds of grapes, which we want to find.

Choosing the Correct Equation

Let's examine the three options:

A. $\frac{1.55}{1}=\frac{x}{3.5}$

B. $\frac{1.55}{1}=\frac{3.5}{x}$

C. $\frac{1.55}{3.5}=\frac{x}{1}$

Analyzing Option A

Option A is $\frac{1.55}{1}=\frac{x}{3.5}$. This equation is saying that the cost of one pound of grapes ($\$1.55$) is equal to the cost of 3.5 pounds of grapes ($x$). This is a correct representation of the problem, as we want to find the cost of 3.5 pounds of grapes.

Analyzing Option B

Option B is $\frac{1.55}{1}=\frac{3.5}{x}$. This equation is saying that the cost of one pound of grapes ($\$1.55$) is equal to the ratio of 3.5 pounds of grapes to the unknown cost ($x$). This is not a correct representation of the problem, as we want to find the cost of 3.5 pounds of grapes, not the ratio of 3.5 pounds to the cost.

Analyzing Option C

Option C is $\frac{1.55}{3.5}=\frac{x}{1}$. This equation is saying that the cost of one pound of grapes ($\$1.55$) divided by 3.5 is equal to the cost of 3.5 pounds of grapes ($x$). This is not a correct representation of the problem, as we want to find the cost of 3.5 pounds of grapes, not the ratio of the cost to 3.5.

Conclusion

Based on our analysis, the correct equation is option A: $\frac{1.55}{1}=\frac{x}{3.5}$. This equation correctly represents the problem and allows us to find the cost of 3.5 pounds of grapes.

Solving the Equation

To solve the equation, we can cross-multiply:

$1.55 \times 3.5 = x \times 1$

$5.425 = x$

So, the cost of 3.5 pounds of grapes is $\$5.425$.

Conclusion

In conclusion, the correct equation to find the cost of 3.5 pounds of grapes is $\frac{1.55}{1}=\frac{x}{3.5}$. This equation correctly represents the problem and allows us to find the cost of 3.5 pounds of grapes.

Final Answer

The final answer is $\boxed{5.425}$.

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Understanding Equivalent Ratios

When dealing with ratios, it's essential to understand that equivalent ratios have the same value, but the numbers may be different. In this case, we're given the cost of one pound of grapes, which is $\$1.55$. We need to find the cost of 3.5 pounds of grapes using a pair of equivalent ratios.

Q&A Guide

Q: What is the cost of one pound of grapes?

A: The cost of one pound of grapes is $\$1.55$.

Q: How do we find the cost of 3.5 pounds of grapes?

A: We can use a pair of equivalent ratios to find the cost of 3.5 pounds of grapes. The first ratio is the cost of one pound of grapes, which is $\$1.55$. The second ratio is the cost of 3.5 pounds of grapes, which we want to find.

Q: What is the correct equation to find the cost of 3.5 pounds of grapes?

A: The correct equation is $\frac{1.55}{1}=\frac{x}{3.5}$. This equation correctly represents the problem and allows us to find the cost of 3.5 pounds of grapes.

Q: How do we solve the equation?

A: To solve the equation, we can cross-multiply:

$1.55 \times 3.5 = x \times 1$

$5.425 = x$

So, the cost of 3.5 pounds of grapes is $\$5.425$.

Q: What is the final answer?

A: The final answer is $\boxed{5.425}$.

Common Mistakes

Mistake 1: Choosing the wrong equation

Some people may choose the wrong equation, such as option B or option C. However, the correct equation is option A: $\frac{1.55}{1}=\frac{x}{3.5}$.

Mistake 2: Not cross-multiplying

Some people may not cross-multiply the equation, which can lead to an incorrect solution. However, cross-multiplying is a crucial step in solving the equation.

Mistake 3: Not checking the units

Some people may not check the units of the equation, which can lead to an incorrect solution. However, checking the units is an essential step in solving the equation.

Conclusion

In conclusion, the correct equation to find the cost of 3.5 pounds of grapes is $\frac{1.55}{1}=\frac{x}{3.5}$. This equation correctly represents the problem and allows us to find the cost of 3.5 pounds of grapes. By following the steps outlined in this Q&A guide, you can avoid common mistakes and find the correct solution.

Final Tips

• Always choose the correct equation.
• Always cross-multiply the equation.
• Always check the units of the equation.

By following these tips, you can ensure that you find the correct solution to the problem.