SOLUTION: at a birthday party for 20 people each person could order a hot dog or a bucket of chips. if there were four times as many hot dogs as buckets of chips calculate how many hot dogs

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Question 1137031: at a birthday party for 20 people each person could order a hot dog or a bucket of chips. if there were four times as many hot dogs as buckets of chips calculate how many hot dogs and how many buckets of chips were bought
need to write this and solve via simultaneous equations
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
it sounds like each person could order either a hot dog or a bucket of chips but not both.

therefore the total of hot dogs plus chips must equal to 20.

let h = the number of hot dogs and b = the number of buckets of chips, and you get h + b = 20.

since the number of hotdogs ordered was 4 times the number buckets of chips orders, you get h = 4b.

those are your two equations that need to be solved simultaneously.

h + b = 20
h = 4b

in the first equation, replace h with 4b and you get 4b + b = 20.

combine like terms to get 5b = 20.

solve for b to get b = 20/5 = 4.

the number of buckets of chips ordered was 4.

since h = 4b, then the number of hot dobs ordered was 16.

h + b = 16 + 4 = 20.

h = 4b.

the solution is cofirmed to be good based on the problem statements.

the solution is that 16 hot dogs and 4 buckets of chips were ordered.


Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
Let H be the number of hot dogs and C be the number of chips.


Then from the condition we have this system of 2 equations


H + C = 20     (1)    (same as the number of people)

H = 4C         (2)    (four times as many hot dogs as buckets of chips)


From equation (2), substitute the expression H = 4C into equation (1)


4C + C = 20,

5C     = 20,

C      = 20/5 = 4.


ANSWER.  4 buckets of chips and 4*4 = 16 hot dogs.

Solved.


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