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Puzzle Three

Answer the following word problems. Use your answers to substitute into the code below to unlock puzzle three. Remember the order of operations to correctly break the code!

A. Charlie wakes up in the morning and it is 72 degrees outside. A cold front comes in and the temperature drops 34 degrees, and then rises 12 degrees at the end of the day. What is the temperature at the end of the day?

B. Pablo’s Pizza Shop made a profit of $495 each day for twelve days. What was the total profit for all twelve days?

C. Samantha had $299 in her bank account. If she goes shopping and spends $348, what will the balance in her bank account be?

D. A rollercoaster rises 210 feet into the air, drops 80 feet before rising 240 feet, and then drops another 30 feet. The rollercoaster drops another 50 feet. What is the height of the drop after the last rise?

The local grocery store is running a special: Three dozen eggs cost $1.08. What is the cost per egg?

Code: A(D – C) + (B – E)

Math in the Midwest 2019

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08:30

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reducesto $1 .$ It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?(ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?(iii) The sum of the digits of a two-digit number is 9 . Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.(iv) Meena went to a bank to withdraw $? 2000$. She asked the cashier to give her $? 50$ and $? 100$ notes only. Meena got 25 notes in all. Find how many notes of $? 50$ and $? 100$ she received.(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid $? 27$ for a book kept for seven days, while Susy paid $? 21…

23:03

In an old puzzle attributed to Alcuin of York $(735-804),$ a farmer needs to carry a wolf, a goat, and a cabbage across a river. The farmer only has a small boat, which can carry the farmer and only one object (an animal or a vegetable). He can cross the river repeatedly. However, if the farmer is on the other shore, the wolf will eat the goat, and, similarly, the goat will eat the cabbage. We can describe each state by listing what is on each shore. For example, we can use the pair $(F G, W C)$ for the state where the farmerand goat are on the first shore and the wolf and cabbage are on the other shore. [The symbol $\emptyset$ is used when nothing is on a shore, so that $(F W G C, \emptyset)$ is the initial state. $]$a) Find all allowable states of the puzzle, where neither the wolf and the goat nor the goat and the cabbage are left on the same shore without the farmer.b) Construct a graph such that each vertex of this graph represents an allowable state and the vertices repres…

06:38

Solve each problem.Several years ago, mathematical ecologists created a model to analyze population dynamics of the endangered northern spotted owl in the Pacific Northwest. The ecologists divided the female owl population into three categories: juvenile (up to $1 \text { yr old }),$ subadult $(1$ to 2 yr old ) and adult (over 2 yr old). They concluded that the change in the makeup of the northern spotted owl population in successive years could be described by the following matrix equation.$$\left[\begin{array}{c}j_{n+1} \\s_{n+1} \\a_{n+1}\end{array}\right]=\left[\begin{array}{rrr}0 & 0 & 0.33 \\0.18 & 0 & 0 \\0 & 0.71 & 0.94\end{array}\right]\left[\begin{array}{c}j_{n} \\s_{n} \\a_{n}\end{array}\right]$$The numbers in the column matrices give the numbers of females in the three age groups after $n$ years and $n+1$ years. Multiplying the matrices yields the following.$j_{n+1}=0.33 a_{n}$Each year 33 juvenile females are born for each 100 adult females.$s_{n+1}=0…

01:53

Crossword Puzzle: In the $2 \times 2$ box shown here, each answer must be correct four ways: horizontally, vertically, diagonally, and by itself. Instead of words, use symbols of elements. When the puzzle is complete, the four spaces will contain the overlapping symbols of 10 elements. There is only one correct solution.$$\begin{array}{|l|l|}\hline 1 & 2 \\\hline 3 & 4 \\\hline\end{array}$$Horizontal$1-2:$ two-letter symbol for a metal used in ancient times$3-4:$ two-letter symbol for a metal that burns in air and is found in Group $5 \mathrm{A}$Vertical $1-3:$ two-letter symbol for a metalloid $2-4:$ two-letter symbol for a metal used in U.S. coinssingle squares: All one-letter symbols1: a colorful nonmetal2: colorless, gaseous nonmetal3: an element that makes fireworks green4: an element that has medicinal usesDiagonal$1-4:$ two-letter symbol for an element used in electronics$2-3:$ two-letter symbol for a metal used with Zr to make wires for superconducting magnetsT…

Transcript

Use your answers to substitute into the code below to unlock the puzzle. three. Remember the order of operations to correctly break the code. So Charlie wakes up in the morning and it is 72° outside A cold front comes in and the temperature drops 34°. So 72 drops 34°. So 72 minus 34 is 38 And then rises 12° by the end of the day. So if it rises then it goes up to 50. What is the temperature at the end of the day? So 50°. All right, Pablo’s pizza shop made a profit of $495 each day for 12 days. What is the total profit for 12 days? So 495 times 12 is 5940. So 5940. Samantha had 299 in her bank account, goes shopping and spends $348. What is the balance in her bank account? That’s not good. 299 -348 is going to be, she’s going to be in the negative $49. A rollercoaster rises 210 ft in the air Dropth 240 ft. So now it’s at negative 30 ft rises 80 ft, so that’s 50 Before dropping another 30 ft again. So that’s 20. Finally,…

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