Question

Seiji and Gavin both worked hard over the summer. Together they earned a total of $450. Gavin earned $30 more than seiji.

(a) Write a system of equations for the situation. Use s for the amount Seiji earned and g for the amount Gavin earned.

(b) Graph the equations in the system.

(c) Use your graph to estimate how much each person earned around.

Answer 1

(a)
`s+g=450\\g=s+30`

(b) The graph is shown below.

(c) Seiji earned $ 210 and Gavin earned $ 240.

Explanation:

Given:

Sum of earnings of Seiji and Gavin = $ 450

Gavin earns $ 30 more that that of Seiji.

(a)

So, as per question, if s and g are the amounts earned by Seiji and Gavin respectively, then;

`s+g=450\\g=s+30`

(b)

The graph is plotted using the x and y intercepts of each line.

For the line,
`s+g=450`, the x intercept is at
`g=0`. So, x intercept is (450,0). Similarly, the y intercept is when s=0, which is (0,450). Draw a line passing through these two points. The red line represents
`s+g=450`.

We follow the same process to plot the next line. The x intercept is at (-30,0) and y intercept is at (0,30). Draw a line passing through these two points. The blue line represents
`g=s+30`.

The graph is shown below.

(c)

From the graph, the point of intersection of the two lines gives the earnings of each of the persons.

The
`x` value of the point of intersection is the earning of Seiji which is $ 210 and the
`y` value is the earning of Gavin which is $ 240 as shown in the graph.

Therefore, Seiji earned $ 210 and Gavin earned $ 240.