A brooch is made with silver wire in the form of a circle with diameter 42 mm. The wire is also used in...

Question

24. A brooch is made with silver wire in the form of a circle with diameter 42 mm. The wire is also used in making 3 diameters which divide the circle into 6 equal sectors. Find the total length of silver wire.
25. Solve the following pair of linear equations:
0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3

SnapAndSolve AI · Accepted Answer

First, calculate the circumference of the circle using the formula C = πd, where d is the diameter. Here, d = 42 mm, so C = π × 42 mm = 132 mm (approximately).
Next, calculate the total length of the 3 diameters. Each diameter is 42 mm, so 3 diameters = 3 × 42 mm = 126 mm.
The total length of silver wire = circumference + length of 3 diameters = 132 mm + 126 mm = 258 mm.
To solve the equations, use the method of substitution or elimination.
Multiply the first equation by 2 to align the coefficients of x:
0.4x + 0.6y = 2.6
0.4x + 0.5y = 2.3
Subtract the second equation from the first:
0.1y = 0.3
y = 3
Substitute y = 3 into the first equation:
0.2x + 0.3(3) = 1.3
0.2x + 0.9 = 1.3
0.2x = 0.4
x = 2
The solution is x = 2, y = 3.

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A brooch is made with silver wire in the form of a circle with diameter 42 mm. The wire is also used in...

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