Question

Three brothers spent different amounts of money on their recent vacation. Matt spent $25 less than Todd. Jeff spent 3 times as much as Matt. How much did each brother spend if they spent a total of $275?

Answer 1

Let

M = amount of money Matt spent
J = amount of money Jeff spent
T = amount of money Todd spent

Answer 2

if "Matt spent $25 less than Todd", then we cay say that

M = T - 25

Answer 3

if "Jeff spent 3 times as much as Matt", then we know

J = 3*M

Answer 4

"they spent a total of $275", so we can say

M+J +T = 275

Answer 5

how do we find the variables?

Answer 6

now use the 3 equations together to solve

M+J+T = 275 ... start with the 3rd equation

M+3M+T = 275 ... plug in J = 3M (replace J with 3M)

4M+T = 275 ... Combine like terms.

4(T-25)+T = 275 ... plug in M = T - 25 (replace M with T-25)

4T-100+T = 275 ... distribute

I'll let you finish up

Answer 7

notice how all 3 equations were involved and how we went from an equation with 3 variables to an equation with one variable

Answer 8

so does todd equal x?

Answer 9

todd is T

Answer 10

what do you get when you solve 4T-100+T = 275 for T

Answer 11

1275

Answer 12

that's too high

Answer 13

5t-100=275

Answer 14

so far, so good, keep going

Answer 15

its a decimal right?

Answer 16

no, it's a whole number

Answer 17

i got 25.4..

Answer 18

WAIT

Answer 19

sorry i typed 27 lol

Answer 20

5t-100=275

5t-100+100=275+100 ... Add 100 to both sides.

5t+0 = 375 ... Combine like terms.

5t = 375

t = ???

Answer 21

ah i gotcha

Answer 22

t=75.

Answer 23

good, so Todd spent $75

Answer 24

now that you know that T = 75, you can use this and the other equations to find M and J

Answer 25

so we add all the answers up or subtract?

Answer 26

what were the 3 original equations

Answer 27

since T = 75 and we have the equation M = T - 25, we can say this

M = T - 25

M = 75 - 25 .... replace T with 75 (since T = 75)

M = 50

So Matt spent $50

Answer 28

m= t-25
3xm
m+j+t

Answer 29

but i thought matt was 45?

Answer 30

J = 3*M

J = 3*50 ... replace M with 50 (since we now know that M = 50)

J = 150

So Jeff spent $150

Answer 31

Summary:

Todd spent $75
Matt spent $50
Jeff spent $150

Answer 32

not sure how you got $45

Answer 33

damn girllllll..... you shouldnt be talking to this loser you should kik me ;)

Answer 34

i thought matt's equation was m-25,

Answer 35

SwoleNerd this is a study site, not facebook

Answer 36

and i dont have kik.

Answer 37

lol girl how old are you im 15

Answer 38

ok jim i have another question.

Answer 39

Matt's equation is M = T - 25

Answer 40

replace T with 75 (remember we found that T = 75) and you'll get M = 50

Answer 41

ok i got it.

Answer 42

god bless!

Answer 43

what's your other question?

Answer 44

its really long so hold on.

Answer 45

alright

Answer 46

At the end of the lacrosse season, the coach always posts the names of the top 5 scorers and the number of goals each person scored throughout the season. this year, the coach, who is also a math teacher, decided to have some fun with his players. this is what he posted.

Answer 47

Erin scored the least number of goals.
Macy scored 4 times as many goals as Erin.
Carly scored 2 goals less than Macy.
Shelly scored one half as many goals as carly.
Molly scored 1 more goal than Macy.

Answer 48

If the total number of team goals for the season was 253, determine how many goals each of the top 5 players scored.

Answer 49

hello

Answer 50

sorry still reading and thinking

Answer 51

let's start by setting up variables

Let

E = number of goals Erin scored
Ma = number of goals Macy scored
C = number of goals Carly scored
S = number of goals Shelly scored
Mo = number of goals Molly scored

Answer 52

"Macy scored 4 times as many goals as Erin."

means

Ma = 4*E

Answer 53

"Carly scored 2 goals less than Macy."

means

C = Ma - 2

Answer 54

"Shelly scored one half as many goals as carly."

means

S = C/2

Answer 55

"Molly scored 1 more goal than Macy."

means

Mo = Ma + 1

Answer 56

"the total number of team goals for the season was 253"

so we know that

E + Ma + C + S + Mo = 253

Answer 57

because Ma = 4*E, we can solve for E to get

E = Ma/4

Answer 58

E + Ma + C + S + Mo = 253

E + Ma + C + S + Ma + 1 = 253 ... plug in Mo = Ma + 1

E + Ma + C + C/2 + Ma + 1 = 253... plug in S = C/2

E + Ma + Ma - 2 + (Ma - 2)/2 + Ma + 1 = 253... plug in C = Ma - 2

Ma/4 + Ma + Ma - 2 + (Ma - 2)/2 + Ma + 1 = 253... plug in E = Ma/4

Ma/4 + 3*Ma + (Ma - 2)/2 - 1 = 253

Ma/4 + 3*Ma + Ma/2 - 2/2 - 1 = 253

Ma/4 + 3*Ma + Ma/2 - 1 - 1 = 253

Ma/4 + 3*Ma + Ma/2 - 2 = 253

Ma/4 + 12*Ma/4 + 2Ma/4 - 2 = 253

(Ma + 12*Ma + 2Ma)/4 - 2 = 253

(15Ma)/4 - 2 = 253

(15Ma)/4 = 253+2

(15Ma)/4 = 255

15Ma = 255*4

15Ma = 1020

Ma = 1020/15

Ma = 68

So Macy scored 68 points

E = Ma/4

E = 68/4

E = 17

Erin scored 17 points

Mo = Ma + 1

Mo = 68 + 1

Mo = 69

Molly scored 69 points

C = Ma - 2

C = 68 - 2

C = 66

Carly scored 66 points

S = C/2

S = 66/2

S = 33

Shelly scored 33 points


Summary:

E = 17
Ma = 68
C = 66
S = 33
Mo = 69