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A deli offers two platters of sandwiches. Platter A has 2 roast

beef sandwiches and 3 turkey sandwiches. Platter B has

3 roast beef sandwiches and 2 turkey sandwiches. (Platter A= $31.00 Platter B= $29.00)


a. Model with Math Write a system of equations to

represent the situation.


b. What is the cost of each sandwich?

User Nana Kwame
by
3.4k points

2 Answers

4 votes

Answer:

Platter A = 2x + 3y =31

Platter B = 3x + 2y =29

Turkey. Sandwich is $5 each

Beef sandwich is $8 each

step explanation:

let's represent beef with x and turkey with y

Platter A = 2x + 3y =31

Platter B = 3x + 2y =29

To get the cost of each sandwich we should solve the simultaneous equation

2x +3y = 31.... equation 1

3x + 2y = 29 .....equation 2

Solve for y in equation 1

2x +3y = 31

3y = 31- 2x

y =( 31 - 2x)/3

Substitute for y in equation 2

3x + (31 - 2x) /3 = 29 multiply through by 3

9x + 31- 2x = 87 group the equation

9x - 2x = 87 - 31

7x = 56

x = 56/7

x = 8

Substitute for x in equation 1

2x +3y = 31

2(8) + 3y = 31

16 +3y = 31

3y = 31- 16

=15

y = 15/3

y = 5

User Dennislloydjr
by
4.1k points
7 votes

Answer:

Answer a

Following is the equation system.

Equation 1:
2x+3y=31$

Equation 2 :
3x+2y=29\\$

Answer (b)

Cost of Roaster beef sandwich = 5$

Cost of Roaster turkey sandwich = 7$

Explanation:

Part a

Let

x= roasted beef sandwich

y=turkey sandwich

Equation for platter A will be

Equation 1:
2x+3y=31$

Equation for Platter B will be

Equation 2 :
3x+2y=29\\$

Part b

We will solve both equations simultaneously.

Multiply Equation 1 with 2.


2(2x+3y)=2*31\\4x+6y=62

Similarly multiply Equation 2 with 3


3(3x+2y)=29*3\\9x+6y=87

Now subtract Equation 3 from equation 4


(9x+6y)-(4x+6y)=87-61\\9x-4x+6y-6y=25\\5x=25\\x=25/5\\x=5

Now putting the value of x in eq # 1


2x+3y=31\\2(5)+3y=31\\10+3y=31\\3y=31-10\\3y=21\\y=21/3\\y=7

User Masoud Andalibi
by
2.9k points