Question

Solve each of the following problems using a system of equations. Show all of your work and state your solution in a complete sentence.

1.)Tony and Belinda have a combined age of 56. Belinda is 8 more than twice Tony’s age. How old is each?

2.)Salisbury High School decided to take their students on a field trip to a theme park. A total of 150 people went on the trip. Adults pay $45.00 for a ticket and students pay $28.50 for a ticket. How many students and how many adults went to the park if they paid a total of $4770?
can someone please help please??

Answer 1

1. t + b = 56
b = 2t + 8
can you solve this with substitution ?

Answer 2

just sub in 2t + 8 in for b in the 1st equation to solve for t. Once you have t, you can sub it in to the 2nd equation to find b.

Answer 3

2. a + s = 150 --> a = 150 - s
45a + 28.5s = 4770
now sub 150 - s in for a into the 2nd equation to find s. Once s is found, sub that back into the first equation to find a.

Answer 4

I don't know how to do the solving, I am having trouble with that part

Answer 5

1. t + b = 56
b = 2t + 8
we will sub 2t + 8 in for b in the 1st equation
t + (2t + 8) = 56
can you solve this ?

Answer 6

let me try

Answer 7

t+10t=56

Answer 8

no....combine like terms
t + 2t + 8 = 56
3t + 8 = 56
you cannot add 2t + 8 because they are not like terms
now we will subtract 8 from both sides because we want 2t by itself.
3t + 8 - 8 = 56 - 8
combine like terms
3t = 56 - 8
3t = 48
now we will divide by 3 to get t by itself
3t/3 = 48/3
t = 16
do you understand ?

Answer 9

Yes. I
forgot that

Answer 10

so now that we know t = 16, we can sub that into the 1st equation:
t + b = 56
16 + b = 56
can you solve for b now ?

Answer 11

just subtract 16 from both sides

Answer 12

let me know what you get

Answer 13

40

Answer 14

you got it.....Tony is 16 and Belinda is 40

Answer 15

you want to work on the next one now ?

Answer 16

yes please

Answer 17

a + s = 150 (adults + students = 150)
45a + 28.5s = 4770 (45 for adult tickets + 28.5 for student tickets = 4770)
do you understand how I got the equations ?
Because setting up the equation is the hardest part.

Answer 18

yes

Answer 19

now we will isolate a variable in the first equation...it doesn't matter which one, so which one do you want to isolate ? Your choice.....a or s ?

Answer 20

A

Answer 21

a + s = 150 --> a = 150 - s
understand ?

Answer 22

I just subtracted s from both sides to get a by itself

Answer 23

I understand

Answer 24

now we will sub 150 - s in for a in the 2nd equation...
45a + 28.5s = 4770
45(150 - s) + 28.5s = 4770
do you know how to distribute the 45 through the parenthesis ?

Answer 25

you * 45 by 150 and s

Answer 26

yes...but it is a -s not just an s

Answer 27

so what did you get ?

Answer 28

i don't understand. i am still working

Answer 29

you need help ?

Answer 30

45*150=6750
did i do that right?

Answer 31

yes....now do 45 * -s

Answer 32

or you could just leave the - in and do 45 *s

Answer 33

i need help with this part

Answer 34

45(150 - s) + 28.5s = 4770
6750 - 45s + 28.5s = 4770
Understand ?

Answer 35

i don't understand

Answer 36

which part....the distribution part ?

Answer 37

the hole thing

Answer 38

all we are doing is subbing in 150 - s in for a. Do you understand how we got the 150 - s ?

Answer 39

no

Answer 40

a + s = 150
we want to isolate a variable.....you chose to isolate a, to do this we must subtract s from both sides.
a + s - s = 150 - s
the s's on the left side cancel out, leaving us with a = 150 - s.
Do you understand ?

Answer 41

yes

Answer 42

our 2nd equation is 45a + 28.5s = 4770
we will sub 150 - s in for a
45(150 - s) + 28.5s = 4770
are you with me so far ?

Answer 43

yes

Answer 44

i get it now

Answer 45

now we will distribute...
45(150 - s) + 28.5s = 4770
45 * 150 - 45*s + 28.5s = 4770
6750 - 45s + 28.5s = 4770
now can you combine like terms ?

Answer 46

150-28.5=121

Answer 47

no......
6750 - 16.5s = 4770
what I did was combined my s terms ... -45s + 28.5s = -16.5s
Understand ?

Answer 48

yes

Answer 49

now we have 6750 - 16.5s = 4770
we want -16.5s on one side and everything else on the other side. So we need to subtract 6750 from both sides.
6750 - 6750 - 16.5s = 4770 - 6750
this cancels out the 6750 on the left side leaving us with :
-16.5s = 4770 - 6750
you still with me ?

Answer 50

yes

Answer 51

dont forget, what you do on one side of the equal sign, you have to do on the other side.
-16.5s = -1980
now we will divide both sides by -16.5 to get s by itself
-16.5s/-16.5 = -1980/-16.5
s = -1980/-16.5
can you find s now ?

Answer 52

remember a negative divided by a negative is a positive

Answer 53

120

Answer 54

so s = 120
now sub 120 in for s in the equation a + s = 150

Answer 55

30

Answer 56

yes....a = 30
let me check out answers to see if they are correct...hold on

Answer 57

okay. thank you for your help!!! :)

Answer 58

45a + 28.5s = 4770
45(30) + 28.5(120) = 4770
1350 + 3420 = 4770
4770 = 4770 (correct)

adult tickets 30
student tickets 120

Answer 59

glad I could help :)

Answer 60

:)