1. Unit 5. Day 6.

2. Equation Pattern 6
$ 24 4 𝑠𝑜𝑐𝑘𝑠
$ 𝑠𝑜𝑐𝑘 𝐷 = 6 ∙ 𝑠

3. Equation Pattern
3 4 𝑚𝑖 ℎ𝑟
3 2
𝑚𝑖 1 ℎ𝑟
3 2 𝐷 = ∙ 𝑡

4. Equation Pattern
1.60
€ 8 5 𝑘𝑔
€ 𝑘𝑔 𝐸 =
1.6 ∙ 𝑘

5. Equation Pattern
2 5
2 𝑝𝑖𝑧𝑧𝑎𝑠 5 𝑡𝑒𝑒𝑛𝑠
𝑝𝑖𝑧𝑧𝑎𝑠 1 𝑡𝑒𝑒𝑛
2 5 𝑃 = ∙ 𝑡

6. Groups

7. Example A: Jackson and his grandfather constructed a model for a birdhouse. Many of their neighbors offered to buy the birdhouses. Jackson decided that building birdhouses could help him earn money for his summer camp, but he is not sure how long it will take him to finish all of the requests for birdhouses. If Jackson can build 7 birdhouses in 5 hours, write an equation that will allow Jackson to calculate the time it will take him to build any given number of birdhouses, assuming he works at a constant rate.

8. Example A: Jackson can build 7 birdhouses in 5 hr.
a) Write an equation that you could use to find out how long it will take him to build any number of birdhouses.
b) How many birdhouses can Jackson build in 40 hours?   
c) How long will it take Jackson to build 35 birdhouses? Use the equation from part (a) to solve the problem.
 d) How long will it take to build 71 birdhouses? Use the equation from part (a) to solve the problem.

9. Example A: Jackson can build 7 birdhouses in 5 hours.
a) Write an equation that you could use to find out how long it will take him to build any number of birdhouses. 7
7 5
𝑏𝑖𝑟𝑑ℎ𝑜𝑢𝑠𝑒 ℎ𝑜𝑢𝑟 ÷5
𝑏𝑖𝑟𝑑ℎ𝑜𝑢𝑠𝑒 ℎ𝑜𝑢𝑟
𝑏𝑖𝑟𝑑ℎ𝑜𝑢𝑠𝑒 ℎ𝑜𝑢𝑟 5 ÷5
5 7
ℎ𝑜𝑢𝑟 𝑏𝑖𝑟𝑑ℎ𝑜𝑢𝑠𝑒 5 ÷7
0.714… 𝑏𝑖𝑟𝑑ℎ𝑜𝑢𝑠𝑒 ℎ𝑜𝑢𝑟
ℎ𝑜𝑢𝑟 1 𝑏𝑖𝑟𝑑ℎ𝑜𝑢𝑠𝑒 7 ÷7
7 5
5 7 𝐵 = ∙ 𝐻 𝐻 = ∙ 𝐵

10. b) How many birdhouses can Jackson build in 40 hours?
𝐵= 7 5 𝐻
𝐵= 7 5
= 5 7 𝐵
𝐻= 5 7 𝐵
b) How many birdhouses can Jackson build in 40 hours? 𝐵= 40 40
5 7
5 7
𝐵= 280 5
40 1
7 5
5 7 40 ÷ ∙ = 𝐵
280 5 56 = 𝐵
𝐵=56

11. c) How long will it take Jackson to build 35 birdhouses?
= 7 5 𝐻
𝐵= 7 5 𝐻
𝐻= 5 7 𝐵
𝐻= 5 7
c) How long will it take Jackson to build 35 birdhouses? 𝐻= 35 35
7 5
7 5
𝐻= 175 7
35 1
7 5
5 7 35 ÷ ∙ = 𝐻
175 7
𝐻=25 25 = 𝐻

12. d) How long will it take Jackson to build 71 birdhouses?
= 7 5 𝐻
𝐵= 7 5 𝐻
𝐻= 5 7 𝐵
𝐻= 5 7
d) How long will it take Jackson to build 71 birdhouses? 𝐻= 71 71
7 5
7 5
𝐻= 355 7
71 1
7 5
5 7 71 ÷ ∙ = 𝐻
355 7
50 5 7
𝐻=50 5 7 = 𝐻

13. Barbara’s Produce Stand
Example B: Al’s Produce Stand sells 6 ears of corn for $ Barbara’s Produce Stand sells 13 ears of corn for $ Write two equations, one for each produce stand, that model the relationship between the number of ears of corn sold and the cost. Then, use each equation to help complete the tables below.
Al’s Produce Stand
Barbara’s Produce Stand
Ears 6 14 21 13
Cost
$1.50
$50.00
$3.12
$49.92
$ 𝑒𝑎𝑟
1.50
$ 𝑒𝑎𝑟
3.12 6 13

14. Barbara’s Produce Stand
Al’s Produce Stand
Barbara’s Produce Stand
Ears 6 14 21 13
Cost
$1.50
$50.00
$3.12
$49.92 𝑥 𝑦
$ 𝑒𝑎𝑟
$ 𝑒𝑎𝑟
$ 𝑒𝑎𝑟 ÷6
0.25
÷13
$ 𝑒𝑎𝑟
0.24 ÷6
÷13 C
ost =
0.25 ∙ 𝑒
𝑎𝑟𝑠 C
ost =
0.24 ∙ 𝑒
𝑎𝑟𝑠 𝑦 =
0.25𝑥
𝑦=0.24𝑥 . 2 5 . 2 4 6 13 2 − −
1 2
2 6 3 5 − − 30 52

15. Barbara’s Produce Stand
Al’s Produce Stand
Barbara’s Produce Stand
Ears 6 14 21 13
Cost
$1.50
$50.00
$3.12
$49.92 𝑥 14 21 14 21 𝑦 50
49.92
𝐶=0.25𝑒
𝐶=0.24𝑒
𝑦=0.25𝑥
𝑦=0.24𝑥 𝐶
=0.25 𝑒 𝐶
=0.24 𝑒
0.25
0.25
0.24
0.24 𝐶=
3.50
5.25 𝐶=
3.36
5.04
200=𝑒
200
208=𝑒
208