Question

Systems of Equation Task

Answer 1

Priya: S=20w+50

Vanessa: S=25w+20

6 weeks

Explanation:

`\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}`

Part a

Define the variables:

• Let w be the number of weeks.
• Let S be the total savings (in dollars).

Given that Priya starts with $50 in her bank account, the y-intercept of the linear equation modelling her savings will be 50.

If she then deposits $20 each week for 12 weeks, the slope will be 20.

Therefore, the linear equation that models Priya's savings is:

• 
  `S=20w+50`

Given that Vanessa starts with $20 in her bank account, the y-intercept of the linear equation modelling her savings will be 20.

If she then deposits $25 each week for 12 weeks, the slope will be 25.

Therefore, the linear equation that models Vanessa's savings is:

• 
  `S=25w+20`

Part b

Create a table for each linear equation from part a.

Priya Vanessa

`\begin{array}\cline{1-2} w & S \\\cline{1-2} 1&70 \\\cline{1-2} 2& 90\\\cline{1-2} 3&110 \\\cline{1-2} 4&130 \\\cline{1-2} 5& 150\\\cline{1-2} 6&170 \\\cline{1-2} 7&190 \\\cline{1-2} 8&210 \\\cline{1-2} 9&230 \\\cline{1-2} 10&250 \\\cline{1-2} 11& 270\\\cline{1-2} 12& 290\\\cline{1-2} \end{aligned}`
`\begin{array}c\cline{1-2} w & S \\\cline{1-2} 1&45 \\\cline{1-2} 2& 70\\\cline{1-2} 3& 95\\\cline{1-2} 4& 120\\\cline{1-2} 5& 145\\\cline{1-2} 6& 170\\\cline{1-2} 7& 195\\\cline{1-2} 8& 220\\\cline{1-2} 9& 245\\\cline{1-2} 10& 270\\\cline{1-2} 11& 295\\\cline{1-2} 12&320 \\\cline{1-2} \end{aligned}`

Create a graph for each linear equation (see attachment).

Part c

The week in which Priya and Vanessa will have the same amount of savings is the week where the S-values in the tables are the same, and the point of intersection of the graphed lines.

Therefore, from inspection of the tables and graphs from part b, Priya and Vanessa will have the same amount of savings in week 6.