# solving problems

<object:standard:macc.912.a-ced.1.1 macc.912.a-rei.2.3=””>1. Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water.

Part A: Write an equation in one variable that can be used to find the total number of liters of lemon juice and water in the bottle. Define the variable used in the equation.

Part B: How many liters of lemon juice are present in the bottle? Show your work.

2 .Jake is comparing the prices of two laundry service companies. Company A charges $20 per load and an additional $8 as service charges. Company B charges $24 per load and an additional $4 as service charges.

Part A: Write equations to represent Company A’s and Company B’s total laundry charges for a certain number of loads. Define the variable used in the equations.

Part B: Which company would charge less for 5 loads of laundry? Justify your answer.

C: How much money is saved by using the services of Company A instead of Company B to clean 9 loads of laundry?

3. Emily uses her college photocopier machine to photocopy at the rate of $0.08 per page. She decides to rent a photocopier machine for $90 a year. The cost of photocopying using the rented machine is $0.03 per page.

Part A: Write an inequality that can be used to calculate the number of pages that Emily should photocopy in a year so that the amount she pays for the rented machine is less than the college machine. Define the variable used.

Part B: How many pages should Emily print in a year to justify renting the photocopier? Show your work.

4.In a certain town, the barometric inches of air pressure, x, on a certain day is described by two statements:

- If 3 times the air pressure is increased by 2, the pressure is still less than 92 inches.
- Twice the air pressure minus 39 is greater than 11 inches.

Part A: Create a compound inequality to represent the air pressure range.

Part B: Can the air pressure in this town be 24 inches? Justify your answer by solving the inequalities in Part A.

Part C: The average air pressure in another town is 29 inches, but the actual pressure is within 4 inches of the average. Write and solve an inequality to find the range of air pressure in this town.

5.Part A: Solve C = (F – 32) for F.

<object:standard:macc.912.a-rei.2.3; macc.912.a-ced.1.4=””>Part B: Determine the value of F when C = 8 °C.

Part C: Solve –np – 80 > 60 for n. Show your work.

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