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jeyben [28]
3 years ago
14

at a concession stand, seven hot dog(s) and four hamburger(s) cost $18.25; four hot dog(s) and seven hamburger(s) cost $17.50. F

ind the cost of one hot dog and the cost of one hamburger. What is the cost of one hot dog?
Mathematics
1 answer:
horsena [70]3 years ago
6 0

The cost of one hot dog is $1.75

The cost of one hamburger is $1.5

<u>Step-by-step explanation</u>:

Let,

  • The cost of hot dog be 'x'.
  • The cost of hamburger be 'y'.

The equations can be formed as :

7x + 4y = 18.25  --------(1)

4x + 7y = 17.50  --------(2)

Multiply eq (1) by 4 and eq (2) by 7,

   28x + 16y = 73

- (<u>28x + 49y = 122.5)</u>

  <u>        - 33y = - 49.5</u>

y = 49.5/33

y = 1.5

The cost of one hamburger is $1.5

Substitute y=1.5 in eq (1),

7x + 4(1.5) = 18.25

7x = 18.25 - 6

x = 12.25/7

x = 1.75

The cost of one hot dog is $1.75

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Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,169 was collected on the sale of 1,325 ticket
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Answer:

461 adults and 864 students

Step-by-step explanation:

We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 1,325 tickets were purchased, then s+a=1325.

We also know that a total of $3,169 was collected and adult tickets cost $5 each and students cost $1 each. We can write 1s+5a=3169.

We will solve by substituting one equation into the other. We first solve the first equation for s which is s=1325-a. Substitute s=1325-a into 1s+5a=3169. Simplify and isolate the variable a.

1(1325-a)+5a=3169

1325-a+5a=3169

1325+4a=3169

1325-1325+4a=3169-1325

4a=1844

a=461

This means that 461 adults attended and 864 students attended since 864+461=1325.

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