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On a long-distance bus service, 10% of the passengers held VIP passes and also brought pets aboard. If 70% of the passengers with VIP passes did not bring pets, what percent of the bus’s passengers held VIP passes?

Explanation	Calculations	Help
$We first create an unknown for the percentage of passengers who held VIP passes.$	$R = percent of passengers with VIP passes$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "70% of the passengers with VIP passes did not bring pets", which implies the remaining percent of those passengers did bring pets.$	$R - \frac{70}{100} R = \frac{30}{100} R$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We translate "10% of the passengers held VIP passes and also brought pets aboard" as the fraction of all passengers who both held VIP passes and brought pets.$	$\frac{30}{100} R = \frac{10}{100}$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We solve the equation for the unknown by isolating the variable.$	$\frac{30}{100} R = \frac{10}{100} R = \frac{\frac{10}{100}}{\frac{30}{100}} = \frac{10}{30} = \frac{1}{3} = 33 \frac{1}{3} %$

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C

On a long-distance bus service, 10% of the passengers held VIP passes and also brought pets aboard. If 70% of the passengers with VIP passes did not bring pets, what percent of the bus’s passengers held VIP passes?

Explanation	Calculations	Help
$We first create an unknown for the percentage of passengers who held VIP passes.$	$R = percent of passengers with VIP passes$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "70% of the passengers with VIP passes did not bring pets", which implies the remaining percent of those passengers did bring pets.$	$R - \frac{70}{100} R = \frac{30}{100} R$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We translate "10% of the passengers held VIP passes and also brought pets aboard" as the fraction of all passengers who both held VIP passes and brought pets.$	$\frac{30}{100} R = \frac{10}{100}$	Theory & Tactics Method Card TRANS2-A Click to view full details
$We solve the equation for the unknown by isolating the variable.$	$\frac{30}{100} R = \frac{10}{100} R = \frac{\frac{10}{100}}{\frac{30}{100}} = \frac{10}{30} = \frac{1}{3} = 33 \frac{1}{3} %$

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C