During a football game, a concession stand sold a family 2 hamburgers and 2 hotdogs for a total of $13. It sold another family 2 hamburgers and 5 hotdogs for a total of $16. What are the prices of a hamburger and a hotdog?

The price of each hamburger is $3

The price of each hot dogs is $2  .

Step-by-step explanation:

Given as :

The total price of 3 hamburger and 2 hot dogs = $13

The total price of 2 hamburger and 5 hot dogs = $16

Let The price of each hamburger = $x

Let The price of each hot dogs = $y

Now, According to question

3 x + 2 y = 13              A

2 x + 5 y = 16              B

Now, Solving to eq A and B

3 × (2 x + 5 y ) - 2 × (3 x + 2 y ) = 3 × 16 - 2 × 13

Or, (6 x + 15 y) - (6 x + 4 y) = 48 - 26

Or, (6 x - 6 x) + (15 y - 4 y) = 22

Or, 0 + 11 y = 22

∴  y =

i.e y = $2

so, The price of each hot dogs = y = $2

Now, Put the value of y into eq B

i.e 2 x + 5 y = 16

or, 2 x + 5 × 2 = 16

or, 2 x = 16 - 10

or, 2 x = 6

∴  x =

i.e x = $3

So, The price of each hamburger = x = $3

Hence, The price of each hamburger is $3 and  The price of each hot dogs is $2  . Answer

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for