linear equations?

Question

m=7n
3m+8n-29

a sightseeing boat charges $5 for children and $8 for adults.On its first trip of the dat, it collected $439 for 71 paying passengers.How many children and adults were there?

Answer 1

m=7n
3(7n)+8n=29n
if your sum is 3m+8n-29=0 then n=1
if it is 3m+8n=-29 then n=-1
depending on n m will be 7 or -7

2.5C+8A=439
C+A=71
-5C-5A=-355 multiplying by -5
adding
3A=84
A=28
C=43
so 28 adults and 43 children

Answer 2

You need to set up two equations with 2 variables each.

If you know 439 was collected, then you can make the equation

439 = 5c + 8a.

You also know that 71 passengers went on the boat,
so c + a = 71.

You know need to uses substitution to solve.

439 = 5c + 8a
c + a = 71

Take one equation and solve for one of the variable. The second one looks simpler, so I'll do that.

c + a = 71
c = 71 - a.

When you get that, plug it into the other equation.

439 = 5c + 8a.
439 = 5 (71 - a) + 8a.

Now solve.

439 = 355 - 5a + 8a
439 = 355 + 3a
439 - 355 = 3a
84 = 3a
28 = a

Now plug this back into one of the equations to solve for the other variable.

c + a = 71.
c + 28 = 71
c = 43.

So, there were 43 children and 28 adults.

Answer 3

by solving simultaneous equations or substitution;
C= number of children
A= number of adults
C+A=71 (or A=71-C)
5C+8A=439
substituting A from the first eq. into the second;
solve for C, then for A
5C+8(71-C)=439 ; 568-3C=439 ; C=43 ; A=28

Answer 4

let x be the number of children
let y be the number of adults

x+y=71 now y=71-x and sub into 5x+8y=439
5x+8(71-x)=439
5x+568-8x=439
-3x=439-568
-3x=-129
x=-129 / -3
x=43
so there were 43 children there and also
x+y=71
43+y=71
y=71-43
y=28
28 adults

Answer 5

c=# of children
a=# of adults

We have
8a+5c=439
a+c=71

So 5a+5c=355
Then 3a=84, so a=28, and c=43. To check

28+43=71
8*28+5*43=439

Steve

Answer 6

28 adults and 43 children.