tanvi is collecting pledges for a walk - a - thon. her mother has pledged a flat donation of $10, and her…

tanvi is collecting pledges for a walk - a - thon. her mother has pledged a flat donation of $10, and her grandmother has pledged $2 per kilometer. if tanvi walks a certain distance, the two donors will end up owing the same amount. how much will each donor owe? write a system of equations, graph them, and type the solution.

tanvi is collecting pledges for a walk - a - thon. her mother has pledged a flat donation of $10, and her grandmother has pledged $2 per kilometer. if tanvi walks a certain distance, the two donors will end up owing the same amount. how much will each donor owe? write a system of equations, graph them, and type the solution.

Answer

Explanation:

Step1: Define the equations

Let $x$ be the distance in kilometers and $y$ be the amount of donation. The mother's donation equation is $y = 10$ (a flat - donation, no dependence on distance). The grandmother's donation equation is $y=2x$.

Step2: Find the intersection point

Set the two equations equal to each other: $2x = 10$. Solve for $x$: $x=\frac{10}{2}=5$. Substitute $x = 5$ into either equation to find $y$. Using $y = 2x$, we get $y=2\times5 = 10$. To graph $y = 10$, it is a horizontal line passing through the point $(0,10)$ on the $y$ - axis. To graph $y = 2x$, the $y$ - intercept is $0$ and the slope is $2$. We can plot the points $(0,0)$ and $(1,2)$ and draw a line through them.

Answer:

The solution is $x = 5$ kilometers and $y=10$ dollars. So each donor will owe $10$ dollars.