# Mathematics Support

Algebra I | Unit 1 2 3 4 5 6 7

## LINEAR EQUATIONS, INEQUALITIES AND SYSTEMS

### Videos

In this unit, your student will analyze constraints on different quantities. For example, the amount you spend on groceries may be limited by your budget. To qualify for a sports team, you may need to practice at least a certain number of hours, or lift at least a certain number of pounds. Here are some ways to write constraints using mathematical notation: w<20. An apartment building only allows dogs that weigh less than 20 pounds. m+g+b=4. A casserole recipe calls for four cups of vegetables. You have mushrooms, green beans, and broccoli. 12.5c+15a=1,000. In order for a concert to be performed, the artists need to be sure of 1,000 in ticket sales. Tickets for children under 18 are 12.50 and tickets for adults are 15.5n + 10d = 150. You need 1.50 in coins for a parking meter. You have a bunch of nickels and dimes in your pocket. For this last situation, we can see that using more dimes to make $1.50 means that we can use fewer nickels, and vice-versa. A graph allows us to see this relationship even more clearly. Each point on the graph represents a combination of nickels and dimes that totals$1.50. For example, if you use 8 nickels, you will need 11 dimes.

Priya is saving money to go on an overnight school trip. The cost of the trip is 360. She has a job at a convenience store, which pays 9 per hour, and sometimes babysits for a family in her neighborhood, which pays 12 per hour. The equation 9x + 12y = 360 represents all the combinations of hours Priya could work at each job and earn a total of 360. Here is a graph showing those combinations.

1. What are the coordinates of point A?
2. What does it tell us about the number of hours Priya worked at each job?
4. Point D is not on the line. How should we interpret point D?
5. Point E is not on the line. How should we interpret point E? ### Solution

1. (20,15)
2. Priya works 20 hours at the convenience store and 15 hours babysitting.
3. Point B: (36,6). Priya works 32 hours at the convenience store and 6 hours babysitting. Point C: (40,0). Priya works 40 hours at the convenience store and does not babysit at all.
4. Priya does not make enough money. She works 24 hours at the convenience store and 8 hours babysitting. She makes only $312, since 24·9+8·12=312. 5. Priya makes more than enough money:$438. She works 30 hours at the convenience store and 14 hours babysitting. 30·9+14·12=438.