Exam 2: Simplifying Expressions

Simplify both sides of the equation as much as possible, and then solve.

For the graph below, write an inequality whose solution is the graph.

Tyler is taking piano lessons. Because he doesn't practice as often as his parents would like him to, he has to pay for part of the lessons himself. His parents pay him $0.75 to do the laundry and $1.25 to mow the lawn. In one month, he does the laundry 6 more times than he mows the lawn. If his parents pay him $16.50 that month, how many times did he mow the lawn?

Suppose you have $7.20 in dimes and quarters. How many of each coin do you have if you have twice as many quarters as dimes?

Solve the equation.

In a right triangle, one of the acute angles is five times as large as the other acute angle. Find the measure of the two acute angles.

Travis has a savings account that his parents opened for him. It pays 8% annual interest. His uncle also opened an account for him, but it pays 10% annual interest. If there is $550 more in the account that pays 8%, and the total interest from both accounts is $170, how much money is in each of the accounts? $ __________ invested at 8% $ __________ invested at 10%

Solve the equation. = __________

Solve the equation.

An accountant has money in three accounts that pay 6%, 10%, and 12% in annual interest. He has twice as much invested at 6% as he does at 10% and three times as much invested at 12% as he does at 10%. If the total interest from the three accounts if $232 for the year, how much is invested at each rate? ( Hint : Let = the amount invested at 10%.) $ __________ invested at 6% $ __________ invested at 10% $ __________ invested at 12%

Ike and Nancy Lara give western dance lessons at the Elk's Lodge on Sunday nights. The lessons cost $3.00 for members of the lodge and $4.00 for nonmembers. Half of the money collected for the lesson is paid to Ike and Nancy. The Elk's Lodge keeps the other half. One Sunday night Ike counts 40 people in the dance lesson. What is the least amount of money Ike and Nancy will make?

When Kate exercises, she either swims or runs. She wants to spend a minimum of 6 hours a week exercising, and she wants to swim 2 times the amount she runs. What is the minimum amount of time she must spend doing each exercise? At least __________ hours running and __________ hours swimming.

Recently, the Texas Junior College Teachers Association annual conference was held in Austin. At that time a taxi ride in Austin was $1.25 for the first of a mile and $0.50 for each additional of a mile.If the distance from one of the convention hotels to the airport is 8 miles, how much will it cost to take a taxi from that hotel to the airport?

Simplify both sides as much as possible, and then solve.

Diane is 30 years older than her daughter Amy. In 2 years Diane will be twice as old as Amy. How old are they now?

Solve the equation. __________

The length of a rectangle is 2 feet less than 2 times the width. The sum of the length and width is 16 more than the width. Find the width.

If the temperature on the ground is , then the temperature at feet above the ground can be found from the expression Find the temperature at an altitude of 24,000 feet.

Simplify both sides as much as possible, and then solve. __________

Solve the equation.