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 Calculate Maze Begin at the key marked ‘START’ and carry out the calculation as indicated. Once you have got that answer, find that corresponding number on a different key. On that different key calculate its answer and with this new number proceed to the next key. Continue on in this way until you eventually find a number that does not lead anywhere else. What is that final numbered key? Boxed in? A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, what is the maximum width which is allowed for this box? What’s the angle? In the figure below, RT = TU. What is the value of x⁰ ?

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### Roman Arithmetic

Roman Arithmetic is the use of arithmetical operations on Roman Numerals.  Roman numerals are a numeral system of ancient Rome based on letters of the alphabet, which are combined to signify the sum or difference of their values. The Romans depicted numbers using seven letters of the alphabet as numerals:   I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 & M = 1000. The system does not include a zero and is shown from 1 to 10 as: I, II, III, IV, V, VI, VII, VIII, IX and X.  Symbols are written and read from left to right, from highest to lowest values. A letter placed after another of greater value adds (e.g., XVI is 16 and the year 2022 in Roman Numerals is MMXXII) whereas a letter placed before another of greater value subtracts (e.g., XC is 90). With this brief introduction, solve the following expressions and state their results in Roman Numerals.

Solution:

1. IV + XCIX = CIII
4 + 99 = 103
2. LXX + CLXX = CCXL
70 + 170 = 240
3. LIV – XLIV + CLIV = CLXIV
54 – 44 + 154 = 164
4. MV – CCCXC – DLII = LXIII
1005 – 390 – 552 = 63
5. LXXV + CXIX + DCCXVI = CMX
75 + 119 + 716 = 910
6. XI + XXII + XXXIII + XLIV – LV = LV
11 + 22 + 33 + 44 – 55 = 55
7. DIII + XDXII + CMXXIV + CLXXI = MMX
503 + 412 + 924 + 171 = 2010
8. MDCCLXV – MCXX + DXLIV – CDXCVI = DCXCIII
1765 – 1120 + 544 – 496 = 693

### Time calculation

A watch gains 20 seconds every half hour. It was last set at 3pm.  What is the actual time, to the nearest minute, when it reads 3pm on the next day?

Solution:

24 hrs. x (1/3 min. / ½hr.) x 2 half hrs. / hr.= 48 / 3 = 16 minutes
Therefore, actual time next day equals 3pm – 16 min. = 2:44 pm

### Sequencing

What comes next in this mathematical sequence:

1, 6, 21, 66, 201, 606, 1821, ?

Solution: 5466 is the next number in the sequence

Each successive number in the sequence is arrived at by multiplying the current one by three, then adding three.

(1 x 3) + 3 = 6 …  …  … (1821 x 3) + 3 = 5466