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A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

Explanation	Calculations	Help
$We first create clear variables for the 1996 revenues using non-ambiguous names.$	$C = revenue from car sales in 1996 T = revenue from truck sales in 1996$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the phrase "revenues from car sales in 1997 were down 11 percent from 1996" into a relative decrease of 11%.$	$0.89 C = revenue from car sales in 1997$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate the phrase "revenues from truck sales in 1997 were up 7 percent from 1996" into a relative increase of 7%.$	$1.07 T = revenue from truck sales in 1997$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate the phrase "total revenues from car sales and truck sales in 1997 were up 1 percent from 1996" by summing the 1997 revenues and setting it equal to a 1% increase on the 1996 total.$	$0.89 C + 1.07 T = 1.01 \times (C + T)$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS2-D Click to view full details
$We then solve that equation to find the ratio C : T .$	$0.89 C + 1.07 T = 1.01 C + 1.01 T - 0.12 C = - 0.06 T 0.12 C = 0.06 T \frac{C}{T} = \frac{0.06}{0.12} = \frac{1}{2}$

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A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

Explanation	Calculations	Help
$We first create clear variables for the 1996 revenues using non-ambiguous names.$	$C = revenue from car sales in 1996 T = revenue from truck sales in 1996$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the phrase "revenues from car sales in 1997 were down 11 percent from 1996" into a relative decrease of 11%.$	$0.89 C = revenue from car sales in 1997$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate the phrase "revenues from truck sales in 1997 were up 7 percent from 1996" into a relative increase of 7%.$	$1.07 T = revenue from truck sales in 1997$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate the phrase "total revenues from car sales and truck sales in 1997 were up 1 percent from 1996" by summing the 1997 revenues and setting it equal to a 1% increase on the 1996 total.$	$0.89 C + 1.07 T = 1.01 \times (C + T)$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS2-D Click to view full details
$We then solve that equation to find the ratio C : T .$	$0.89 C + 1.07 T = 1.01 C + 1.01 T - 0.12 C = - 0.06 T 0.12 C = 0.06 T \frac{C}{T} = \frac{0.06}{0.12} = \frac{1}{2}$

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