The relationships between x, the number of weeks, and y, the number of miles Jiro and Trina bike each week, are graphed on the coordinate plane below. What is the point of intersection?
Jiro
Trina
0
1
2
3
4
5
6
7
8
9
10
0
20
40
60
80
100
120
140
160
180
200
Time (weeks)
Number of miles
The point of intersection is (
,
).
Great job!
Now that you have found the point of intersection, (2, 80), let’s check that work algebraically. The equations for the relationship between weeks and miles for Jiro and Trina are shown below. Since the number of miles Jiro bikes will be equal to the number of miles Trina bikes at the solution to this system, you can set the expression for the number of miles they each bike, 60+10x and 120−20x, equal to one another. Do that now.
Jiro
Trina
0
1
2
3
4
5
6
7
8
9
10
0
20
40
60
80
100
120
140
160
180
200
Time (weeks)
Number of miles
60+10x
=
120−20x
Nice!
Let’s solve the equation for x, the number of weeks when Jiro and Trina bike the same number of miles, to confirm that it’s the same as the x-coordinate of the point of intersection. Since there are x terms on both sides of the equation, let’s get rid of the x term from one of the sides. What move can you make to get rid of the x term on the right side of the equation, 20x, while keeping the equation balanced?
Jiro’s miles = Trina's miles
60+10x = 120−20x
Subtract 20x from each side
Multiply each side by 20x
Add 20x to each side
1 answer
To simplify the equation \( 60 + 10x = 120 - 20x \) and eliminate the \( x \) term on the right side, you want to get rid of the \( 20x \) on that side. The best move to do that while keeping the equation balanced is:
Subtract \( 20x \) from each side.
So the equation will be transformed like this:
\[ 60 + 10x + 20x = 120 - 20x + 20x \]
This simplifies to:
\[ 60 + 30x = 120 \]
Now, you can proceed with solving for \( x \). Would you like to continue solving for \( x \)?
