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3) Fill in the blanks using the available answer choices. The total cost is \( \qquad \) to the number of lunches bought because (Blank 1 ) the ratios between the quantities \( \qquad \) the same (Blank 2) unit rate. Blank 1 options - proportional Blank 2 options - not proportional - are all equal and have - are not equal and do not have 4) Fill in the blanks using the available answer choices. A saltwater solution for an aquarium calls for 35 parts salt to 1000 parts water. Tareq used 7 tablespoons of salt and 200 tablespoons of water. This situation \( \qquad \) a proportional relationship because (Blank 1) (Blank 2) Blank1 options - represents - does not represent Blank 2 options - both have a ratio of 7:200 - both have a ratio of 3 : 125 - the ratios are different

Ask by Chang Henry. in the United States
Mar 14,2025

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1. The total cost is **proportional** to the number of lunches bought because the ratios between the quantities **are all equal and have** a unit rate. 2. This situation **represents** a proportional relationship because **both have a ratio of 7:200**.

Solución

1. For the statement \[ \text{The total cost is } \underline{\textbf{proportional}} \text{ to the number of lunches bought because the ratios between the quantities } \underline{\textbf{are all equal and have}} \text{ unit rate.} \] Step-by-step reasoning: - The cost increases at the same rate as the number of lunches, which means they are in a proportional relationship. - This holds when the ratios (cost per lunch) are all equal. 2. For the saltwater solution problem: Tareq’s solution uses 7 tablespoons of salt and 200 tablespoons of water. The aquarium recipe calls for 35 parts salt to 1000 parts water. Note that \[ \frac{35}{1000} = \frac{7}{200} \] Thus the ratio in the recipe simplifies exactly to the ratio Tareq used. So we fill in the blanks as \[ \text{This situation } \underline{\textbf{represents}} \text{ a proportional relationship because } \underline{\textbf{both have a ratio of }7:200}. \] Step-by-step reasoning: - The given salt-to-water ratio simplifies from \(\frac{35}{1000}\) to \(\frac{7}{200}\). - Tareq's mixture exactly matches the simplified ratio, confirming the proportionality.

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The total cost is proportional to the number of lunches bought because the ratios between the quantities are all equal and have a unit rate. This means that as you increase the number of lunches, the total cost increases in a consistent manner, making budgeting easier! In Tareq's case, this situation does not represent a proportional relationship because the ratios are different. While he used 7 tablespoons of salt and 200 tablespoons of water, those amounts don't match the original ratio of 35 parts salt to 1000 parts water, leading to an incorrect salt concentration for the aquarium!

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