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Make Small Machines Safer We know that making school shops safe is not easy. Our SENSING-SAF-START ® helps by making small machines (like table saws and band saws) safer by preventing them from restarting after a power interruption. You can go to our web site jdsproducts.com and order from one of our distributors like Midwest Technology Products. monthly marketplace LUCIFER Economy Red Devil Series t Low Cost, Top Quality Furnaces t Easy to Operate t Harden, Draw & Anneal POSTERS for STEM & CTE Classrooms www.techdirections.com/ posters.html t Temps to 2200° F t Ideal for Schools, R&D (800) 378-0095 www.luciferfurnaces.com Buy from tech directions advertisers. They make your subscription possible. for the top and bottom sides equal to each other: (x + 8) + (x + 12) = (x + 3) + (x + 2) + (2x + 3) 2x + 20 = 4x + 8 2x = 12 x = 6 Now go back and substitute 6 for x in all the expressions for the sides. The dimensions of the rectangle are 33 × 32. State of the Estate There were six sons and the estate consisted of 36 coins. Let G = total number of gold coins and N = total number of sons. We know the first son gets 1 gold coin and 1/7 of what is left (which is now [G -1] because he took one. Therefore, the first son gets {1 + (1/7) × (G -1)} gold coins. Simplify the above expression to {6/7 + G/7} We also know the second son gets 2 gold coins and 1/7 of what is left, or {2 + (1/7) × (what is NOW left)} The key is realizing that what is NOW left for the second son is {G -[6/7 + G/7] -2} because it is the total amount minus what the first son took minus the 2 gold coins that the second son took. Therefore the second son receives {2 + (1/7) × (G -6/7 -G/7 -2)}, which simplifies to: 6 × G/49 + 78/49 Set these two expressions equal to one another because we know that each son receives the same amount. 6 × G/49 + 78/49 = 6/7 + G/7 G = 36 gold coins. To find the number of sons, N, note that the first son got 6 gold coins by plugging in G=36 into the first expres-sion 6/7 + G/7. This means that every son received 6 gold coins. 36 total gold coins × 1 son / 6 gold coins = 6 sons. Inventor/Invention Match Up 1 — A 4 — J 7 — F 10 — D 2 — E 5 — H 8 — G 3 — I 6 — B 9 — C Does Anybody Really Know What Time It Is? It is 26 minutes until six o’clock. More than Fun Answers Problems Squared The dimensions of the squares are 1 × 1, 4 × 4, 7 × 7, 8 × 8, 9 × 9, 10 × 10, 14 × 14, 15 × 15, and 18 × 18. To solve, let x = the length of the segment indicated in the diagram below. Then represent the lengths of other segments in the diagram in terms of x. x + 8 x + 8 x + 8 x + 4 x + 8 x + 12 x + 12 x + 12 4 4 4 4 x + 4 x + 4 x + 1 x x + 1 x + 3 1 1 1 x + 1 1 x + 2 x + 3 x + 2 x + 3 x + 2 x + 12 2 x + 3 2 x + 3 2 x + 3 Since the opposite sides of a rect-angle are congruent, you can solve for x by setting the two expressions www.techdirections.com MARKETPLACE 33

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