I love math, and I'm good at it. Daniel has a math talent, too. But today our brains were not functioning in high gear.
Dan's been working through the Algebra 1 Honors Book, and today's lesson was about solving problems with multiple variables. You know, you're given a word problem and need to write the equation(s) and then solve. Knowing how to translate a question into an equation is actually the most important part of this. In math books you can sometimes fiddle around to find the right answer, but in real life the numbers aren't always tidy, so the proper set-up is vital.
Anyway, problem #3 had four variables, and so needed four equations. Daniel tried it, then called for help because the answer was obviously wrong. I helped and it was still wrong. We tried again and it was still wrong. We looked at the solution (thank goodness this answer key SHOWS THE WORK!), and realized we had made the same careless error several times. A truly humbling and time consuming experience. Math was over for the day!
Read on only if you really enjoy algebra:
"Super Suites Hotel has four rates for their 250 basic rooms. Senior citizens pay $35 a night. Businesses pay $45, and coupon-holders pay $40. The standard rate is $50 per night if none of these other rates apply. On New Year's Eve, the hotel's room rates brought in $8640 in income.
The number of rooms sold to senior citizens that night was 10 fewer than the number of standard rooms. The number of business rooms was 8 fewer than the number of coupon-holder rooms sold. Also, the sale of coupon-holder rooms was 10 times less than the number of standard rooms sold. How many rooms were empty on New Year's Eve at Super Suites?"
If you're interested in solving this, put your four starter equations and final answer in the comment section. I'll put the correct answers there later. As a start, we used S for senior, B for business, C for coupon-holder, and R for regular (standard). Our mistake was getting senior and standard partially mixed up--beware!