Lucy works at a car dealership and gets paid $1000 a month, regardless of how many cars she sells. In addition, she gets paid $150 for each car she sells. If Lucy made $2,500 this month, how many cars did she sell? 1. Please create an algebraic equation to determine how many cars Lucy sold? 2. Solve the algebraic equation to find out how many cars Lucy sold this month.
1. Since Lucy gets $1000 a month regardless of how many cars she sells, then $1000 will be a constant* in our equation, and it doesn't need variable notation. Since Lucy will get paid $150 for every car, but the number of cars she sells every month can change, we need to have a variable multiplier (x), which represents the number of cars sold. Since Lucy made $2500 with her base monthly pay ($1000) and her car sells our equation becomes 1000 + 150*x = 2500. Notice there is an addition sign (+) in between 1000 and 150*x because her car sells are adding to her base pay. * A constant is a numerical value that does not change. 2. The main method of solving the equation is to isolate the variable x. First, we subtract 1000 from both sides of the equation. Now we have: 150*x=1500. Since 150 is being multiplied by x, we need to divide both sides by 150. Doing so we determine that x=10. Thus, Lucy sold 10 cars this month.
Bob has 2 dogs, 3 cats, 2 turtles, 1 hamster, 5 action figures, and 4 video game systems. How many pets does he have?
We must use addition to find out how many pets Bob has: 2 dogs + 3 cats + 2 turtles + 1 hamster = 8 pets. NOTE: We do not add 5 action figures and 4 video game systems because those are not pets.
Convert the following equation to slope intercept form: 8x + 2y = 16
Slope intercept form is y=m*x+b, so we need to isolate y. First, subtract 8x from both sides yielding 2y = 16-8x. Then divide both sides by 2, yielding y=8-4x. The slope intercept is y=8-4x , where the slope(m) is 4 and the y intercept(b) is 8.