방정식과 부등식 전체 문제

Your roommate, John, offered to buy household supplies for you and your other roommate. You live near the border of three states, each of which has a different sales tax. The total amount of money spent was $100.75. Your supplies were bought with 5% tax, John’s with 8% tax, and your third roommate’s with 9% sales tax. The total amount of money spent without taxes is $93.50. If your supplies before tax were $1 more than half of what your third roommate’s supplies were before tax, how much did each of you spend? Give your answer both with and without taxes.

Three coworkers work for the same employer. Their jobs are warehouse manager, office manager, and truck driver. The sum of the annual salaries of the warehouse manager and office manager is $82,000. The office manager makes $4,000 more than the truck driver annually. The annual salaries of the warehouse manager and the truck driver total $78,000. What is the annual salary of each of the co-workers?

A local band sells out for their concert. They sell all 1,175 tickets for a total purse of $28,112.50. The tickets were priced at $20 for student tickets, $22.50 for children, and $29 for adult tickets. If the band sold twice as many adult as children tickets, how many of each type was sold?

In a bag, a child has 325 coins worth $19.50. There were three types of coins: pennies, nickels, and dimes. If the bag contained the same number of nickels as dimes, how many of each type of coin was in the bag?

The top three countries in oil consumption in a certain year are as follows: the United States, Japan, and China. In millions of barrels per day, the three top countries consumed 39.8% of the world’s consumed oil. The United States consumed 0.7% more than four times China’s consumption. The United States consumed 5% more than triple Japan’s consumption. What percent of the world oil consumption did the United States, Japan, and China consume?“Oil reserves, production and consumption in 2001,” accessed April 6, 2014, http://scaruffi.com/politics/oil.html.

The top three countries in oil production in the same year are Saudi Arabia, the United States, and Russia. In millions of barrels per day, the top three countries produced 31.4% of the world’s produced oil. Saudi Arabia and the United States combined for 22.1% of the world’s production, and Saudi Arabia produced 2% more oil than Russia. What percent of the world oil production did Saudi Arabia, the United States, and Russia produce?“Oil reserves, production and consumption in 2001,” accessed April 6, 2014, http://scaruffi.com/politics/oil.html.

The top three sources of oil imports for the United States in the same year were Saudi Arabia, Mexico, and Canada. The three top countries accounted for 47% of oil imports. The United States imported 1.8% more from Saudi Arabia than they did from Mexico, and 1.7% more from Saudi Arabia than they did from Canada. What percent of the United States oil imports were from these three countries?“Oil reserves, production and consumption in 2001,” accessed April 6, 2014, http://scaruffi.com/politics/oil.html.

The top three oil producers in the United States in a certain year are the Gulf of Mexico, Texas, and Alaska. The three regions were responsible for 64% of the United States oil production. The Gulf of Mexico and Texas combined for 47% of oil production. Texas produced 3% more than Alaska. What percent of United States oil production came from these regions?“USA: The coming global oil crisis,” accessed April 6, 2014, http://www.oilcrisis.com/us/.

At one time, in the United States, 398 species of animals were on the endangered species list. The top groups were mammals, birds, and fish, which comprised 55% of the endangered species. Birds accounted for 0.7% more than fish, and fish accounted for 1.5% more than mammals. What percent of the endangered species came from mammals, birds, and fish?

Meat consumption in the United States can be broken into three categories: red meat, poultry, and fish. If fish makes up 4% less than one-quarter of poultry consumption, and red meat consumption is 18.2% higher than poultry consumption, what are the percentages of meat consumption?“The United States Meat Industry at a Glance,” accessed April 6, 2014, http://www.meatami.com/ht/d/sp/i/47465/pid/47465.

For the following exercises, determine whether the ordered pair is a solution to the system of equations.

$\begin{array}{c}3x-y=4 \\ x+4y=-3\end{array}$ and $(-1,1)$

For the following exercises, determine whether the ordered pair is a solution to the system of equations.

$\begin{array}{c}6x-2y=24 \\ -3x+3y=18\end{array}$ and $(9,15)$

For the following exercises, use substitution to solve the system of equations.

$\begin{array}{c}10x+5y=-5 \\ 3x-2y=-12\end{array}$

For the following exercises, use substitution to solve the system of equations.

$\begin{array}{c}\frac{4}{7}x+\frac{1}{5}y=\frac{43}{70} \\ \frac{5}{6}x-\frac{1}{3}y=-\frac{2}{3}\end{array}$

For the following exercises, use substitution to solve the system of equations.

$\begin{array}{c}5x+6y=14 \\ 4x+8y=8\end{array}$

For the following exercises, use addition to solve the system of equations.

$\begin{array}{c}3x+2y=-7 \\ 2x+4y=6\end{array}$

For the following exercises, use addition to solve the system of equations.

$\begin{array}{c}3x+4y=2 \\ 9x+12y=3\end{array}$

For the following exercises, use addition to solve the system of equations.

$\begin{array}{c}8x+4y=2 \\ 6x-5y=0.7\end{array}$

For the following exercises, write a system of equations to solve each problem. Solve the system of equations.

A performer charges $C(x)=50x+10,000,$ where $x$ is the total number of attendees at a show. The venue charges $75 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?

For the following exercises, solve the system of three equations using substitution or addition.

$\begin{array}{c}0.5x-0.5y=10 \\ -0.2y+0.2x=4 \\ 0.1x+0.1z=2\end{array}$