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.

Solution

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 $: \[ 35x = 210 \] \[ x = \frac{210}{35} \] \[ x = 6 \]