Question

The walnut Cove Ruritan Club sells hot dogs and drinks from a concession stand at the annual 4th of July parade. Carl bought 5 hot dogs and 3 drinks and paid $13.50. Susan purchased 2 hot dogs and 3 drinks and was charged $9.00. What is the cost of 1 hot dog and what is the cost of 1 drink?

Answer 1

Answer:

The cost of one hot dog is $1.5 and the cost of one drink is $2.

Step-by-step explanation:

Let

h = the cost of a hog dog and d = the cost of a drink

We know from the information given that:

• Carl bought 5 hot dogs and 3 drinks and paid $13.50. This is equal to $5\cdot h +3\cdot d=13.50$

• Susan purchased 2 hot dogs and 3 drinks and was charged $9.00. This is equal to $2\cdot h +3\cdot d=9.00$

So we have a system of equations

$5\cdot h +3\cdot d=13.50\\2\cdot h +3\cdot d=9.00$

We can solve by elimination as follows:

$\mathrm{Multiply\:}5h+3d=13.5\mathrm{\:by\:}2:\\10h+6d=27$

$\mathrm{Multiply\:}2h+3d=9\mathrm{\:by\:}5:\\10h+15d=45$

Subtract $10h+6d=27$ from $10h+15d=45$

$(10h+15d=45) -(10h+6d=27)=\\9d=18$

$\mathrm{Solve}\:9d=18\:\mathrm{for}\:d:\\d=2$

$\mathrm{For\:}10h+6d=27\mathrm{\:plug\:in\:}\quad \:d=2$

$\mathrm{Solve}\:10h+6\cdot \:2=27\:\mathrm{for}\:h:\\h=\frac{3}{2} = 1.5$

Therefore

h = $1.5 and d = $2