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?
All right, So 52 is the word problem that has to do with a system of three equations and three unknowns. The sign of the unknowns are three members. We know the three numbers add up to 1 40 center. We know that the small number is half the middle number and the little numbers large. So let's start out by defining our very bulls. So it's may excuse me with a small, um, Why? Unequal middle and C b the large. Okay, so we know that X plus y plus z equals 1 47 We know that x news. Half of why, and we know why. Chapel. All right, So, um, to do a little bit of substitution here. Um, yes. Uh, if we substitute, um, 1/2 z do a substitution here, we substitute one, Have z for why we get that X is not only 1/2 of why, but it's also 14 See? All right, so now what we have is by substituting these values this for Why Jesus, Laura? Meaning? Substitute this for the why and so this for X. And we'll have one equation that only has two seats for the very day. So one for see is equal to I'm sorry. One Ford C plus one Pepsi. Plus, is it? So asked me. 1 47 All right, Um, let me see 1/2. One board is re force. The force was four horse this seven ports. So we get seven wars, See equals 1 47 by both sides. But for over seven, get Z is equal to one of the seven times for 84. So she is 84. That means why is half of that according to and X is half of that. It could be 21 just to check. Seven, 12 13 14 1 47 Adds up. All right, so good.