Answer:
Given equation:
[tex]200x+80y=1600[/tex]
where:
- x = time Eric runs (in mins)
- y = time Eric walks (in mins)
Part (a)
If Eric runs and walks for a total of 12 minutes, then:
[tex]x+y=12[/tex]
Part (b)
To graph:
- Rewrite both equations to make y the subject
- Find the x-intercept
- Find the y-intercept
- Connect the two points with a straight line
[tex]200x+80y=1600 \implies y=20-\dfrac{5}{2}x[/tex]
[tex]\textsf{x-intercept}: \quad 20-\dfrac{5}{2}x=0 \implies x=8 \implies (8,0)[/tex]
[tex]\textsf{y-intercept}: \quad 20-\dfrac{5}{2}(0)=20 \implies (0,20)[/tex]
[tex]x+y=12 \implies y=12-x[/tex]
[tex]\textsf{x-intercept}: \quad 12-x=0 \implies x=12 \implies (12,0)[/tex]
[tex]\textsf{y-intercept}: \quad 12-0=12 \implies (0,12)[/tex]
Point of intersection (equate equations):
[tex]\begin{aligned}20-\dfrac{5}{2}x &=12-x\\20-12 &=\dfrac{5}{2}x-x\\8&=\dfrac{3}{2}x\\16 &=3x\\x &=\dfrac{16}{3}\end{aligned}[/tex]
[tex]y=12-\dfrac{16}{3}=\dfrac{20}{3}[/tex]
[tex]\implies \left(\dfrac{16}{3},\dfrac{20}{3}\right)[/tex]
The point of intersection tells us that Eric runs for 16/3 mins and walks for 20/3 minutes.
