Algebra homework help

Question

Two measuring sticks are exactly the same length. The scale units on the two sticks are different.Each stick is marked with equally spaced units. The first stick starts at 0 and has 462 marks. The second stick starts at 0 and has 385 marks. Suppose the sticks are lined up so the two zero marks were matched, and the 462 mark and 385 mark were also matched exactly. As you scan the measuring sticks, starting at zero, what is the very next set of marks on the two sticks that match exactly? What other marks match? Use Algebra

That was the problem and I figured out that the measurements were inches and centimeters. 462=38.5 inches and 385=38.5 cm. But I can’t figure out the next set of mark on the two sticks that matches exactly and other marks that also matches. Please help me.

Answer 1

Actually, it does not matter whether the measurements are inches, centimeters, ... or Mickeys. The important concept is that the "two measuring sticks are exactly the same length."

Well, what does that mean??

Suppose (let's make up measurements) that stick A has 462 Ks and that stick B has 385 Ds.

This would mean that:

462K = 385D

2*3*7*11*K = 5*7*11*D [finclude prime factors}

6K = 5D [ " 6 K's equals 5 D's " ]

We can check that:

462 * K = 365 * D

462 * (5D/6) = 365 * D

462 = 365 * (6/5)

462 = 462

So each sixth K mark exactly matches each fifth D mark.

The first place where they exactly match is 6 K and 5 D.

Then:

. . .

Answer 2

The key instruction here is "Use Algebra." Let's call our units x and y. So, the sticks are 462x long and 385y long. What we need to know is "What is the relationship between unit x and unit y? That is, how many x's does it take to make a y. The algebraic equation to describe this relationship is 385y = 462x. Dividing both sides by 385, we get y =1.2x. Each mark on a stick represents another whole unit. So the first mark on the "y" stick is at 1.2 on the x stick. There's no mark there on the "x" stick since 1.2 is more than one but less than two whole units. How about 2 on the y stick. It's opposite about 2.4 (2 x 1.2) on the x stick. If we keep going, we'll see that the first time two marks are opposite each other is the mark at 6x and 5y (5 x 1.2 = 6). So, every 5 marks on the x stick will be opposite another six marks on the x stick. So, the marks that will be opposite each other (other than (0,0) and and (462, 385)) are (6, 5), (12, 10), (18, 15), . . . , (456, 380).

Answer 3

I agree with Mark although I did it a different way.

However, the next aligning marks after 492/385 are 847/770.

Answer 4

462 = (2)(3)(7)(11)

385 = (5)(7)(11)

The first aligning numbers are 77, the GCF.