7th graders: please click on the following link for review problems before the Final Exam on Monday and Tuesday

https://sites.google.com/site/lassmath/my-forms

Problem of the Week

__5/31/19__

**Harry’s Broom**

Harry needed to put his 4-foot long broom in a box. He found a box that was 2 feet long by 3 feet wide, and while his broom didn't fit on the bottom, it did fit in the box. What's the shortest the height of the box could be?

**Solution**

Square root of 3. The shortest height for the box would have the broom lying diagonally. Using the Pythagorean Theorem, the minimum length is the square root of 3.

__5/24/19__

**A Day at the Fairs**

It seems that a humble merchant visited three fairs. At the first fair, early in the morning, he doubled his money selling his products, but spent $30 in food and buying other items.

At midday at the second fair, he tripled his money and spent $54. At the third fair in the afternoon he quadrupled his money but spent $72.

Upon his return home to his wife and ten children, late that day, he counted the money he had in his bag; there was $48.

How much did the man gain or lose during the day?

**Solution**

The merchant gained $19 during the day. The equation to solve is:

48 = 4[3(2x-30) – 54] – 72

x = 29, representing how much money the merchant began the day with. 48 – 29 = $19 gain.

__5/17/19__

**Squares Rectangles and Rhombuses**

All squares are both rectangles and rhombuses. All rhombuses and rectangles are parallelograms. On a sheet of paper Josh draws 19 rectangles, 15 rhombuses, and 7 squares. How man parallelograms did Josh draw?

**Solution**

In a Venn diagram, the area where rectangles and rhombuses overlap represents squares. In this region, there are 7 squares, leaving 12 non-square rectangles and 8 non-square rhombuses for a total of 27 parallelograms.

__5/10/19__

**Fair Die**

A fair die is tossed four times. What is the probability that it lands with either 5 or 6 on top at least once?

**Solution**

65/81 or approximately .80247.

The number of possible ways to roll four dice is 6^{4}, or 1296: six choices for each of the four rolls.

There are four ways to roll a single die once and not get a 5 or 6 (that is, to get a 1, 2, 3, or 4), so the number of ways to roll a die four times and not get a 5 or a 6 is 4^{4}, or 256.

Then 1296 - 256, or 1040, ways (the rest of the possibilities) exist to roll the die four times and get a 5 or 6 at least once.

Therefore, the probability of rolling a die four times and getting a 5 or a 6 at least once is 1040/1296, or 65/81, which is approximately .80247.

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