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?

- anonymous

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- jim_thompson5910

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

- jim_thompson5910

if "Matt spent $25 less than Todd", then we cay say that
M = T - 25

- jim_thompson5910

if "Jeff spent 3 times as much as Matt", then we know
J = 3*M

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## More answers

- jim_thompson5910

"they spent a total of $275", so we can say
M+J +T = 275

- anonymous

how do we find the variables?

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

so does todd equal x?

- jim_thompson5910

todd is T

- jim_thompson5910

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

- anonymous

1275

- jim_thompson5910

that's too high

- anonymous

5t-100=275

- jim_thompson5910

so far, so good, keep going

- anonymous

its a decimal right?

- jim_thompson5910

no, it's a whole number

- anonymous

i got 25.4..

- anonymous

WAIT

- anonymous

sorry i typed 27 lol

- jim_thompson5910

5t-100=275
5t-100+100=275+100 ... Add 100 to both sides.
5t+0 = 375 ... Combine like terms.
5t = 375
t = ???

- jim_thompson5910

ah i gotcha

- anonymous

t=75.

- jim_thompson5910

good, so Todd spent $75

- jim_thompson5910

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

- anonymous

so we add all the answers up or subtract?

- jim_thompson5910

what were the 3 original equations

- jim_thompson5910

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

- anonymous

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

- anonymous

but i thought matt was 45?

- jim_thompson5910

J = 3*M
J = 3*50 ... replace M with 50 (since we now know that M = 50)
J = 150
So Jeff spent $150

- jim_thompson5910

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

- jim_thompson5910

not sure how you got $45

- anonymous

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

- anonymous

i thought matt's equation was m-25,

- jim_thompson5910

SwoleNerd this is a study site, not facebook

- anonymous

and i dont have kik.

- anonymous

lol girl how old are you im 15

- anonymous

ok jim i have another question.

- jim_thompson5910

Matt's equation is M = T - 25

- jim_thompson5910

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

- anonymous

ok i got it.

- anonymous

god bless!

- jim_thompson5910

what's your other question?

- anonymous

its really long so hold on.

- jim_thompson5910

alright

- anonymous

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.

- anonymous

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.

- anonymous

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

- anonymous

hello

- jim_thompson5910

sorry still reading and thinking

- jim_thompson5910

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

- jim_thompson5910

"Macy scored 4 times as many goals as Erin."
means
Ma = 4*E

- jim_thompson5910

"Carly scored 2 goals less than Macy."
means
C = Ma - 2

- jim_thompson5910

"Shelly scored one half as many goals as carly."
means
S = C/2

- jim_thompson5910

"Molly scored 1 more goal than Macy."
means
Mo = Ma + 1

- jim_thompson5910

"the total number of team goals for the season was 253"
so we know that
E + Ma + C + S + Mo = 253

- jim_thompson5910

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

- jim_thompson5910

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

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