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Nookie1986 [14]
4 years ago
11

There are 75 houses in the troll's street. If in every 4th house there is a pink troll, a blue troll in every 6th house and a ye

llow troll in every 8th house, then in how many houses are there all of pink, blue and yellow trolls?
Mathematics
2 answers:
denpristay [2]4 years ago
8 0

Answer:

The answer is 3 houses.

Step-by-step explanation:

This question is based on the Least Common Multiple (LCM) method. We will find the LCM of the numbers 4, 6 and 8.

4 = 2 x 2 = 2^{2}

6 = 2 x 3 = 2 x 3

8 = 2 x 2 x 2 = 2^{3}

So, LCM is = 2^{3}\times3=24

Therefore, at every 24th houses, we will find all three trolls colors.

And 24 is the number of houses we will find all color trolls. Then in a group of 75 houses, it will occur thrice and at every 24th place. Means. 3 houses will have all color trolls.

pogonyaev4 years ago
6 0

Answer:

3 houses have all pink, blue, and yellow.

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Using the Sine rule,

\frac{\sin A}{A}=\frac{\sin B}{B}=\frac{\sin C}{C}\begin{gathered} \text{Let A = 14m,} \\ Substituting the variables into the formula,Where the length of the wires are, AP = xm and BP = ym[tex]\begin{gathered} \frac{\sin80^0}{14}=\frac{\sin40^0}{x} \\ \text{Crossmultiply,} \\ x\times\sin 80^0=14\times\sin 40^0 \\ Divide\text{ both sides by }\sin 80^0 \\ x=\frac{14\sin40^0}{\sin80^0} \\ x=9.14m \end{gathered}

Hence, the length of wire AP (x) is 9.14m.

For wire BP (y)m,

Sum of angles in a triangle is 180 degrees,

A^0+P^0+B^0=180^0\begin{gathered} \text{Where A}^0=\text{ unknown,} \\ P^0=80^0\text{ and,} \\ B^0=40^0 \\ A^0+80^0+40^0=180^0 \\ A^0+120^0=180^0 \\ A^0=180^0-120^0 \\ A^0=60^0 \end{gathered}

Using the side rule to find the length of wire BP,

\begin{gathered} \frac{\sin 60^0}{y}=\frac{\sin 80^0}{14} \\ \text{Crossmultiply,} \\ y\times\sin 80^0=14\times\sin 60^0 \\ \text{Didive both sides by }\sin 80^0 \\ y=\frac{14\times\sin 60^0}{\sin 80^0} \\ y=12.31m \end{gathered}

Hence, the length of wire BP (y) is 12.31m

Therefore, the length of the wires are (9.14m and 12.31m).

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1 year ago
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