Questions: Determine how many weeks Amanda can purchase lunches before her account is depleted: SCHOOL LUNCH Amanda has 210 in her school lunch account. She spends 35 each week on school lunches. The equation y=210-35x represents the total amount in Amanda's school lunch account y for x weeks of purchasing lunches.

Determine how many weeks Amanda can purchase lunches before her account is depleted: SCHOOL LUNCH Amanda has 210 in her school lunch account. She spends 35 each week on school lunches. The equation y=210-35x represents the total amount in Amanda's school lunch account y for x weeks of purchasing lunches.
Transcript text: Determine how many weeks Amanda can purchase lunches before her account is depleted: SCHOOL LUNCH Amanda has $\$ 210$ in her school lunch account. She spends $\$ 35$ each week on school lunches. The equation $y=210-35 x$ represents the total amount in Amanda's school lunch account $y$ for $x$ weeks of purchasing lunches.
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Solution

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Solution Steps

To determine how many weeks Amanda can purchase lunches before her account is depleted, we need to find the value of \( x \) when \( y \) becomes 0. This involves solving the equation \( 210 - 35x = 0 \) for \( x \).

Step 1: Set Up the Equation

We start with the equation that represents the total amount in Amanda's school lunch account after \( x \) weeks: \[ y = 210 - 35x \]

Step 2: Determine When the Account is Depleted

To find out when Amanda's account is depleted, we set \( y = 0 \): \[ 0 = 210 - 35x \]

Step 3: Solve for \( x \)

Rearrange the equation to solve for \( x \): \[ 35x = 210 \] \[ x = \frac{210}{35} \] \[ x = 6 \]

Final Answer

Amanda can purchase lunches for \( \boxed{6} \) weeks before her account is depleted.

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