SOLUTION: A group of students takes their math teacher out for lunch. If five have hamburgers and three have hot dogs, the bill will be $24.25. If three have hamburgers and five have hot d

Question 420062: A group of students takes their math teacher out for lunch. If five have hamburgers and three have hot dogs, the bill will be $24.25. If three have hamburgers and five have hot dogs, the bill be be $21.75. What is the price of the hamburger?
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Hamburgers ----- x
Hotdogs ------------ y
5 x + 3 y = 24.25 .............1
3 x + 5 y = 21.25 .............2

multiply (1)by -5
Multiply (2) by 3
-25 x + -15 y = -121.25
9 x + 15 y = 63.75

Add the two equations

-16 x + 0 y = -57.5

/ -16

x=3.59

plug value of x in (1)

5 x + 3 y = 24.25
17.97 + 3 y = 24.25
3 y = 24.25 + -17.97
3 y = 6.28
y = 2.09

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let cost of a hamburger =
Let cost of a hot dog =
given:
(1) (in cents)
(2) (in cents)
----------------
Multiply (1) by and (2) by
(1)
(2)
Subtract (1) from (2)
(2)
(1)

Plug this into (2)
(2)

The price of a hamburger is $3.50
check:
(1)
(1)
(1)
(1)
OK
RELATED QUESTIONS
solve. a group of students takes their math teacher out for lunch. if five have... (answered by edjones)
A group of students go out for lunch. If two have hamburgers and five have hot dogs, the... (answered by mananth)
A group of Wagner students goes out to lunch. If two have burritos and five have tacos,... (answered by mananth,MathTherapy,josgarithmetic)
A group of students go out to lunch. If two have burritos and five have tacos, the bill... (answered by neatmath)
A math teacher will split her class of 15 students into three groups with five students... (answered by ikleyn,greenestamps)
I have only figured out the first equation of this problem I am having trouble setting up (answered by lwsshak3,macston,addingup)
The Freshman class is organizing a picnic and ordered a total of 1300 hot dogs and... (answered by drj)
1. Solve using a proportion. If 2 out of 36 people have hamburgers for lunch, and... (answered by ikleyn)
1. Solve using a proportion. If 2 out of 36 people have hamburgers for lunch, and... (answered by ikleyn,MathTherapy)