Algebra Trig word problem!
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# Algebra Trig word problem!

[From: ] [author: ] [Date: 11-08-29] [Hit: ]
Find, to the nerest tenth of a centimeter, the maximum width and length of the flag.Perimeter is 70 cm maximum,x = 70 * 19 / 58 = 22.Length = x = 22.......
I am confused on 2 problems!

1. An automoblie manufactur can provide no more than 95 cubic feet of passenger space and luggage space for one line of automoblies. The amount of passenger space must be 75 cubic feet more than the luggahe space. Find the maximum amount of passenger space and of luggage space. Find the maximum amount of passenger space abd of luggage space.

2. For an offical United States flag, the ratio of length to width must be excatly 19;10. A manufacturer plans to produce a United States flag that has a perimeter of no more than 70 centimeters. Find, to the nerest tenth of a centimeter, the maximum width and length of the flag.

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1]
Lets assume luggage space = x
passenger space = 75 cubic feet more than luggage space = x + 75

Total space = luggage space + passenger space = 95 cubic feet
x + x + 75 = 95
2x + 75 = 95
2x = 95-75
x = 10 cubic feet

Luggage space = 10 cubic feet
Passenger space = x + 75 = 10 + 75 = 85 cubic feet

2]
Lets assume length = x
length / width = 19 / 10
x / width = 19 / 10
width = 10x / 19

Perimeter = 2(length + width) = 2(x + 10x/19) = 2(19x + 10x)/19 = 58x/19
Perimeter is 70 cm maximum,

58x/19 = 70
x = 70 * 19 / 58 = 22.9 cm

Length = x = 22.9 cm
Width = 10x/19 = 10 * 22.9 / 19 = 12.1 cm

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P + L <= 95
P = L + 75

L + 75 + L <= 95
2L <= 20
L <= 10 cbft
P = 85 cbft

L + W <= 70
L/W = 19/10
10L = 19W
10(70 - W) = 19W
700 = 29W
W = 24.13 cm
L = 45.86 cm
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