Steve went to the concession stand and bought hamburgers and hot dogs for the kids he brought to watch a baseball game. Each child chose either one hamburger or one hotdog. Hot dogs cost $1.50 each and hamburgers cost $2.75 each. Steve spent a total of $23.75 on 10 kids. (a) Could Steve have bought an equal amount of hamburgers and hot dogs? Justify your answer.

(b) If x represents the number of hotdogs purchased and y represents the number of hamburgers purchased, write a system of equations that models this situation and determine the number of both items bought.

b)

x = 3 hotdogs

y = 7 hamburgers

Step-by-step explanation:

Steve went to the concession stand and bought hamburgers and hot dogs for the kids he brought to watch a baseball game. Each child chose either one hamburger or one hotdog. Hot dogs cost $1.50 each and hamburgers cost $2.75 each. Steve spent a total of $23.75 on 10 kids.

(a) Could Steve have bought an equal amount of hamburgers and hot dogs? Justify your answer.

An

(b) If x represents the number of hotdogs purchased and y represents the number of hamburgers purchased, write a system of equations that models this situation and determine the number of both items bought.

Let:

x = the number of hotdogs purchased y = the number of hamburgers purchased

Since the number of kids = 10

Our system for Equation is given as:

x + y = 10 Equation 1

x = 10 - y

x × $1.50 + y × $2.75 = $23.75

1.5x + 2.75y = 23.75

Let us substitute 10 - y for x in Equation 2

1.5(10 - y) + 2.75 = 23.75

15 - 1.5y + 2.75y = 23.75

- 1.5y + 2.75y = 23.75 - 15

1.25y = 8.75

y = 8.75/1.25

y = 7 hamburgers

Solving for x

x = 10 - y

x = 10 - 7

x = 3 hotdogs

Therefore,

x = 3 hotdogs

y = 7 hamburgers

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47