Your roommate, Sarah, offered to buy groceries for you and your other roommate. The total bill was
$\$ 82 .$ She forgot to save the individual receipts but remembered that your groceries were $\$ 0.05$ cheaper than half of her groceries, and that your other roommates groceries were $\$ 2.10$ more than your groceries. How much was each of your share of the groceries?
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 roommates 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?
At a carnival, $\$ 2,914.25$ in receipts were taken at the end of the day. The cost of a child's ticket was $\$ 20.50$ , an adult ticket was $\$ 29.75$ , and a senior citizen ticket was $\$ 15.25$ . There were twice as many senior citizens as adults in attendance, and 20 more children than senior citizens. How many children, adult, and senior citizen tickets were sold?
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?
All right. So Question 54. Got a word problem again with three variables. Three variables are three different types of animals. So we know that a certain animal shelter there are 350 animals. The rabbits that are in the shelter or, um, are five less than half the number of cats and their 20 more cats than dogs s. So we have to set up our variables. Um, I decided arbitrarily to make sure that to have x equal the rabbits. Why cats and people. The number dogs. All right, so our first equation is gonna be that x plus. Why? What Z equals 3 50 Okay, now the rabbits are five less than half the cats. So the rabbits you won't. Five less than five. Less than half that. Yes. And then finally, there's 20 more tests and dogs case. That means that, um, dogs plus 20 people's cats. So come, basically what we want a deal here is to start substitute into the top equation. So what we already have here is this in or right here? And so it's sending X plus y. It's gonna be 1/2. Why Minors fire men. Plus why and then we want to solve this one for Z so we can service to the Y value for that Z is why minus 20. So for us. Why? Minus 20? He was 35 our 350 50. All right, Um, now, once we have that, uh, let's go here. Combined terms. Eso We've got 122 and 1/2. Five over two. Why? Um You see, we've got minus 25 on this side. So let's had 25 this side that he's 3 75 Multiply both sides reciprocal here. And why equals 375 sounds too, We're told. Love. Oh, turned off 3 75 away. 6 375 3 75 by five times two. Here's 1 50 Okay, so there are 100 and 50 cats. You see, there's that's 20 more and the dogs. Okay, so why minus 20? So 130 you dogs and then half of, um, they have to have 23 fifties of this next class. One has to be seven. The second makes two 1 50 75 50. Just 200 left. Okay. All right. Sorry about that. Okay. Check