438,347 views
6 votes
6 votes
Elena is buying food for a school picnic and has $40 to spend on sandwiches. She can buy 5 turkey sandwiches and 5 avocado sandwiches for $40, or she can buy 6 turkey sandwiches and 3 avocado sandwiches for $39. Based on the prices of these two options, what is the cost of 1 turkey sandwich and 2 avocado sandwiches? Explain.

A.) $8.00
B.) $11.00
C.) $13.00
D.) $16.00

User Mike Farmer
by
3.1k points

2 Answers

14 votes
14 votes

Final answer:

By solving a system of linear equations, we determine the cost of one turkey sandwich is $5 and one avocado sandwich is $3. Hence, the cost of 1 turkey sandwich and 2 avocado sandwiches is $11, which corresponds to answer choice B.

Step-by-step explanation:

The question involves solving a system of linear equations to determine the cost of one turkey sandwich and two avocado sandwiches. We have two equations based on the given scenarios:

  • 5T + 5A = $40 (five turkey sandwiches and five avocado sandwiches)
  • 6T + 3A = $39 (six turkey sandwiches and three avocado sandwiches)

Let's denote the cost of a turkey sandwich as T and the cost of an avocado sandwich as A. We can solve these equations simultaneously to find the values of T and A.

First, we can multiply the first equation by 3 and the second equation by 5, and then subtract the second equation from the first to eliminate A:

  • (3)(5T + 5A) = 3($40)
  • (5)(6T + 3A) = 5($39)

After simplification, we get basic equations:

  • 15T + 15A = $120
  • 30T + 15A = $195

Subtracting the equations, we get:

15T = $75 => T = $5

Now we can substitute T = $5 into one of the original equations to find the value of A:

5T + 5A = $40

5($5) + 5A = $40

$25 + 5A = $40

5A = $15 => A = $3

Therefore, the cost of one turkey sandwich (T) is $5 and the cost of one avocado sandwich (A) is $3. To find the cost of 1 turkey sandwich and 2 avocado sandwiches:

1T + 2A = 1($5) + 2($3) = $5 + $6 = $11

The cost of 1 turkey sandwich and 2 avocado sandwiches is $11.

User Simon Angatia
by
2.8k points
16 votes
16 votes

Answer:A

Step-by-step explanation: Because 40 Divided by 5 is 8

User LonelyWebCrawler
by
2.9k points