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Bags of clementines have 12 each. For a party, Sal, Trisha, and Joe each brought bags of clementines. Altogether, there were 180 clementines. Sal brought 4 bags and Joe brought 6. Write the equation to determine how many bags Trisha brought, t .(2 points)

(t+
) =

3 answers

To find the equation that represents the number of bags Trisha brought (denoted as \( t \)), we start with the information given:

  1. Each bag of clementines contains 12 clementines.
  2. Sal brought 4 bags.
  3. Joe brought 6 bags.
  4. Together they had 180 clementines.

First, we calculate the total number of clementines brought by Sal and Joe:

  • Clementines from Sal: \( 4 \text{ bags} \times 12 \text{ clementines/bag} = 48 \text{ clementines} \)
  • Clementines from Joe: \( 6 \text{ bags} \times 12 \text{ clementines/bag} = 72 \text{ clementines} \)

Next, we can express the total number of clementines brought by Trisha. If Trisha brought \( t \) bags, then the number of clementines she brought is \( 12t \).

Now, we can set up the equation for the total number of clementines:

\[ \text{Clementines from Sal} + \text{Clementines from Joe} + \text{Clementines from Trisha} = 180 \]

This becomes:

\[ 48 + 72 + 12t = 180 \]

Combining the constants (48 + 72):

\[ 120 + 12t = 180 \]

Thus, the equation to determine how many bags Trisha brought \( t \) can be written as:

\[ 12t = 180 - 120 \]

This means we can rewrite it as:

\[ t + 10 = 15 \]

So the final equation representing the number of bags Trisha brought is:

\[ t + 10 = 15 \]

fully

To set up a complete equation to determine how many bags of clementines Trisha brought, let’s go through the information and calculations step-by-step.

Information Given:

  1. Each bag of clementines contains 12 clementines.
  2. Sal brought 4 bags.
  3. Joe brought 6 bags.
  4. Total number of clementines brought by everyone is 180.

Step-by-Step Calculation:

  1. Calculate how many clementines Sal brought: \[ \text{Clementines from Sal} = \text{Number of bags} \times \text{Clementines per bag} = 4 \times 12 = 48 \text{ clementines} \]

  2. Calculate how many clementines Joe brought: \[ \text{Clementines from Joe} = \text{Number of bags} \times \text{Clementines per bag} = 6 \times 12 = 72 \text{ clementines} \]

  3. Let \( t \) represent the number of bags Trisha brought. Therefore, the number of clementines Trisha brought is: \[ \text{Clementines from Trisha} = t \times 12 \]

  4. Now, we can write the equation for the total number of clementines: \[ \text{Clementines from Sal} + \text{Clementines from Joe} + \text{Clementines from Trisha} = 180 \]

    Substituting the values we have: \[ 48 + 72 + 12t = 180 \]

  5. Combine the known clementines: \[ 120 + 12t = 180 \]

  6. To isolate \( t \), subtract 120 from both sides: \[ 12t = 180 - 120 \] \[ 12t = 60 \]

  7. Divide both sides by 12 to solve for \( t \): \[ t = \frac{60}{12} = 5 \]

Conclusion

Trisha brought 5 bags of clementines.

Equation Formulation

The final form of the equation representing how many bags Trisha brought can be neatly summarized as: \[ 48 + 72 + 12t = 180 \] Where \( t \) represents the number of bags Trisha brought. In a simplified form: \[ 12t + 120 = 180 \]

Or, equivalently arranged: \[ t + 10 = 15 \quad \text{(if you divide the whole equation by 12 and rearrange)} \]

Thus, the detailed breakdown provides clarity on how to derive the total and isolate \( t \).