Chapter Closure
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165 bricks
Martin's Equation: y=2x
Horace's Equation: y=165-3x
Table:
| x | Martin | Horace |
|---|---|---|
| 10 | 20 | 135 |
| 20 | 40 | 105 |
| 30 | 60 | 75 |
| 40 | 80 | 45 |
| 50 | 100 | 15 |
Graph:
After 33 minutes they will each have 66 bricks.
We know that it takes Horace 55 minutes to finish tearing down his wall. Additionally, he is able to take down 3 bricks per minute. If he can take down 3 bricks every minute, in 55 minutes he will have taken down 3 times 55 bricks.
We want to represent this situation with equations, tables, and a graph.
Let y represent the number of bricks in the wall and x represent the number of minutes the boys work in slope-intercept form. y=mx+b
We know that Martin lays 2 bricks every minute. Therefore, in x minutes he will lay 2x bricks. Since he is building the wall from scratch, he began with laid bricks, which is the equation's y-intercept. Now we can write Martin's equation.
Since Horace is taking down his wall, his equation will show a decreasing number of bricks. From Part A we know that his wall originally had 165 bricks, which becomes our y-intercept. In 1 minute he takes down 3 bricks, so in x minutes there will be - 3x less bricks in the wall, which becomes our slope. Now we can write Horace's equation. y=- 3x+165
Since we have already found the equations representing this situation, we can make a table of values for each equation!
Let's find the number of bricks after 10, 20, 30, 40, and 50 minutes.
| x | 2x | y |
|---|---|---|
| 10 | 2( 10) | 20 |
| 20 | 2( 20) | 40 |
| 30 | 2( 30) | 60 |
| 40 | 2( 40) | 80 |
| 50 | 2( 50) | 100 |
We will also find the bricks that Martin tears down.
| x | -3x+165 | y |
|---|---|---|
| 10 | -3( 10)+165 | 135 |
| 20 | -3( 20)+165 | 105 |
| 30 | -3( 30)+165 | 75 |
| 40 | -3( 40)+165 | 45 |
| 50 | -3( 50)+165 | 15 |
Having constructed the table, we can plot the ordered pairs in a coordinate plane and connect each set of points with a line.
