algebra homework help?

Question

WRITING SYSTEMS OF LINEAR EQUATIONS
Define the variables, then solve the system. Remeber to answer the question.

An ice skating arena charges an admission fee for each chlid plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented 5 pairs of ice skates.He was charged $32.00. Juanita paid the admission fees for her 7 grandchildren and rented 5 pairs of ice skates. She was charged $35.25. What is the admissions fee? What is the rental fee for a pair of skates?

Answer 1

6a + 5r = 32
7a + 5r = 35.25

Subtract first from second

a = 3.25

Then

6(3.25) + 5r = 32

r = 2.5

So the admission cost is $3.25 and the rental cost is $2.50

Answer 2

Let the admission fee be x and rent be y.
For John it's
6x+5y=32
and for Juanita it's
7x+5y=35.25
Subtracting the first from second equation we get
x=$3.25
substitute the value of x in first equation.
y=$2.5
So the rental fee for a pair of skates is $2.5 and a admission fee
costs $3.25

Answer 3

First assign variables:
Admission Fee = A
Skate Rental Fee = R

Then create equations:

John
6A+5R=32

Juanita
7A+5R=35.25

Then solve:

7A+5R=35.25
-( 6A+5R=32)

A+0R=3.25 or A=3.25

plug A back into either equation and solve for R

7(3.25) +5R = 35.25
22.75+5R=35.25
5R=12.50
R=2.50

Admission Fee $3.25
Skate Rental Fee $2.50

Plug into the other equation to check your work

6A+5R=32
6(3.25)+5(2.50)=32
19.50+12.50=32
32=32

Answer 4

let a = admission fee
let r = rental fee

for John
6a + 5r = $32.00
5r = $32.00 - 6a
for juanita
7a + 5r = $35.25
5r = $35.25 - 7a

solving by substitution:
$32.00 - 6a = $35.25 - 7a
7a - 6a = $35.25 - $32.00
a = $3.25
5r = $32.00 - 6a = $32.00 - $19.50 = $12.5
r = $2.50

5r = $35.25 - 7a = $35.25 - $22.75 = $12.5
r = $2.50

a= $3.25 r = $2.50

Answer 5

letadmissionfee be x and rental for skates be y
6x+5y=32
7x+5y=35.25
subtracting
x=3.25
sub x=3.25 in 6x+5y=32
19.50+5y=32
5y=12.50
y=2.50
so admission fees=$3.25
rental=$2.50

Answer 6

the eqution is n+s-$32 for the 1st one
the second one is g+s=35.25
the answer is the addmission $3.25 the rental is $2.50