Question

1) Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $20 for every 400 envelopes she finishes. Jason earns $10 for every 250 envelopes he finishes.

A) Create tables, draw graphs, and write equations that show the earnings, y, as functions of the number of envelopes stuffed, x, for both Anna and Jason.

Answer 1

The answer is below

Explanation:

A) i)

For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)\\\\y-0=(20-0)/(400-0)(x-0)\\\\y=(1)/(20) x`

The table is:

x: 200 400 600 800 1000

y: 10 20 30 40 50

ii)

For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)\\\\y-0=(10-0)/(250-0)(x-0)\\\\y=(1)/(25) x`

The table is:

x: 200 400 600 800 1000

y: 8 16 24 32 40

The graph is plotted using geogebra online graphing