Question

A group of 40 children attended a baseball game on a field trip. Each child revived either a hot dog or a bag of popcorn. Hot dogs were $2.25 and popcorn was $1.75. if the total bill was $83.50, how many hot dogs and bags of popcorn were purchased? Write the system of equations that models the situation

Answer 1

${\huge {\mathfrak {Answer :-}}}$

➡️ Let, number of hot dog = x.

Number of popcorn = y.

➡️ x + y = 40.

Or, y = 40 - x.

➡️ 2.25x + 1.75y = 83.50

Or, 225x + 175y = 8350.

Or, 225x + 7000 - 175x = 8350.

Or, 50x = 1350.

Or, x = 27.

➡️ Hence, number of hot dog = 27.

Number of popcorn = 40 - 27 = 13.

That's it..

Answer 2

let the no. of hotdogs purchased be x and that of popcorn be y.

2.25(x) + 1.75 (y) =83.50

x +y =40

by eq.2 we can say x=40-y

putting the value of x in eq.1,

2.25(40-y) + 1.75y= 83.5

90-2.25y+1.75y= 83.5

-0.5y=6.5

y=13

x=40-y=40-13=27

so, 27 hotdogs and 13 popcorns were purchased.