A word problem

Question

Mike bought hot dogs and soda's for him and his friends. He bought a total of 18 items. Hot dogs were $1.50 and sodas were $0.75. He spent a total of $21.75. How many hotdogs and sodas did he buy?

Answer 1

Hi Nick.

 

We have

H = # hot dogs

S = # sodas

 

From the second sentence we know Mick bought 18 items.

H + S = 18

 

We also know that hot dog were $1.50 and sodas were $0.75

And from the 3rd sentence, in total he spent $21.75

We can write this as

1.5H + .75S = 21.75

 

Since H+S=18,

H = 18-S

 

We can substitute this for H in our equation.

 

1.5(18-S) + .75S = 21.75

27 - 1.5S + .75S = 21.75

27 - .75S = 21.75

5.25 = .75S

S = 7

 

Also since H = 18-S,

H = 18-7

H = 11

 

So Mike bought 7 sodas and 11 hotdogs.