An architect designing a parking lot has a row of 202 ft wide to divide into spaces for compact cars and full-size cars. The architect determines that 16 compact car spaces and 6 full-size car spaces use the width, or that 12 compact car spaces and 9 full-size car spaces use a width of 201 ft.  What are the widths (to the nearest 0.1 ft) of the spaces being planned?(NOT GRAPHICALLY)

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
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An architect designing a parking lot has a row of 202 ft wide to divide into spaces for compact cars and full-size cars. The architect determines that 16 compact car spaces and 6 full-size car spaces use the width, or that 12 compact car spaces and 9 full-size car spaces use a width of 201 ft.  What are the widths (to the nearest 0.1 ft) of the spaces being planned?(NOT GRAPHICALLY)

 

Expert Solution
Forming the equations from the given information

Let's Assume that the width of Compact sized car is x  and the width of full-size car is y.

According to the Question, 16 compact car spaces and 6 full-size car spaces use the width and in the next case 12 compact car spaces and 9 full-size car spaces use a width of 201 ft.

Forming the Equations  based on the given information  ,we have,

16x+6y=202 ---(1)12x+9y=201 ---(2)

Equation (1) can be reduced to :

8x+3y=101  --(3)

Equation (2) can be reduced to :

4x+3y=67---(4)

 

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