See the attached file pick ONE of the problems that has not

Systems of Equations 1)A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot 1) dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot dogs and 4 bags of potato chips for $9.25. Find the cost of each item. 2) University Theater sold 556 tickets for a play. Tickets cost $22 per adult 2) and $12 per senior citizen. If total receipts were $8492, how many senior citizen tickets were sold? 3 A tour group split into two groups when waiting in line for food at a fast 3) food counter. The first group bought 8 slices of pizza and 4 soft drinks for$36.12. The second group bought 6 slices of pizza and 6 soft drinks 4) Tina Thompson scored 34 points in a recent basketball game without making any 3-point shots. She scored 23 times, making several free throws worth 1 point each and several field goals worth two points each. How many free throws did she make? How many 2-point field goals did she make? 5) Julio has found that his new car gets 36 miles per gallon on the highway and 31 miles per gallon in the city. He recently drove 397 miles on 12 gallons of gasoline. How many miles did he drive on the highway? How many miles did he drive in the city? 6) A textile company has specific dyeing and drying times for its different 6) cloths. A roll of Cloth A requires 65 minutes of dyeing time and 50 minutes of drying time. A roll of Cloth B requires 55 minutes of dyeing time and 30 minutes of drying time. The production division allocates 2440 minutes of dyeing time and 1680 minutes of drying time for the week. How many rolls of each cloth can be dyed and dried?

Solution

1) vendor sells hot dog and bag of potato chips.

customer buys 4 hot dogs and 5 bags of potato chips for $ 12.00

customer buys 3 hot bags and 4 bags of potato chips for $ 9.25

Let the price of hot dog be $x and $y of potato chips bag

So, customer buys 4 hot dogs and 5 bags of potato chips for $ 12.00:

4*x + 5*y = $12.00 ----(1)

3 hot bags and 4 bags of potato chips for $ 9.25

3*x + 4*y = $ 9.25 -----(2)

Solve equation 1 and 2 by elimination method:

multiply equation 1 by 3 and equation 2 by 4:

12x + 15y = 36.00

12x +16y = 37.00

---------------(-)

-y = -1 ; y =1

4x +5y = 12 ; 4x +5*1 = 12

4x = 7 ; x= 7/4

x = 1.75

Price of hot dog $ 1.75 and price of potato chips be $ 1.0