Show the algebraic equations that you use to solve the problems and include all necessary work.?

Question

(1) The relation between Celsius and Fahrenheit scale of temperatures is given by:C = (5/9)(F - 32), or, F = (9/5)C + 32.Calculate the temperature in Celsius if the temperature in Fahrenheit is 45°F. Also, calculate the temperature in Fahrenheit if the temperature in Celsius is 98°C.

(2) The perimeter of a swimming pool is 96m. The width is 3m more than half the length of the pool. Find the length and breadth of the pool.

Answer 1

1)
When F = 45,
C = (5/9)(45 - 32)
C = 5/9(13)
C = 7.2 (to 1 decimal place)

When C = 98,
F = (9/5)(98) + 32
F = 176.4 + 32
F = 208.4


2) Let the length of the swimming pool be x meters,
Breadth will be equal to (1/2)x + 3 meters.

Perimeter = 96
2x length + 2x breadth= 96
2x + 2 ((1/2)x + 3) = 96
2x + x + 6 = 96
3x + 6 = 96
Subtract 6 from both sides: 3x = 90
x = 30

Length of swimming pool is 30m
Breadth of swimming pool is 1/2(30)+3 = 18m.

Answer 2

For question #1, just plug the numbers into the proper formula and work it out. For #2, half the perimeter (48m) is equal to one length plus one width. If you let the length be L, then the width is L/2 + 3, so the equation is (L/2 + 3) + L = 48. Simplify that to 1.5L + 3 = 48, 1.5L = 45, L = 30. That makes the length 30 meters and the width 15+3 = 18 meters.