anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
Let M = amount of money Matt spent J = amount of money Jeff spent T = amount of money Todd spent
jim_thompson5910
  • jim_thompson5910
if "Matt spent $25 less than Todd", then we cay say that M = T - 25
jim_thompson5910
  • jim_thompson5910
if "Jeff spent 3 times as much as Matt", then we know J = 3*M

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jim_thompson5910
  • jim_thompson5910
"they spent a total of $275", so we can say M+J +T = 275
anonymous
  • anonymous
how do we find the variables?
jim_thompson5910
  • 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
  • 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
  • anonymous
so does todd equal x?
jim_thompson5910
  • jim_thompson5910
todd is T
jim_thompson5910
  • jim_thompson5910
what do you get when you solve 4T-100+T = 275 for T
anonymous
  • anonymous
1275
jim_thompson5910
  • jim_thompson5910
that's too high
anonymous
  • anonymous
5t-100=275
jim_thompson5910
  • jim_thompson5910
so far, so good, keep going
anonymous
  • anonymous
its a decimal right?
jim_thompson5910
  • jim_thompson5910
no, it's a whole number
anonymous
  • anonymous
i got 25.4..
anonymous
  • anonymous
WAIT
anonymous
  • anonymous
sorry i typed 27 lol
jim_thompson5910
  • 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
  • jim_thompson5910
ah i gotcha
anonymous
  • anonymous
t=75.
jim_thompson5910
  • jim_thompson5910
good, so Todd spent $75
jim_thompson5910
  • jim_thompson5910
now that you know that T = 75, you can use this and the other equations to find M and J
anonymous
  • anonymous
so we add all the answers up or subtract?
jim_thompson5910
  • jim_thompson5910
what were the 3 original equations
jim_thompson5910
  • 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
  • anonymous
m= t-25 3xm m+j+t
anonymous
  • anonymous
but i thought matt was 45?
jim_thompson5910
  • 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
  • jim_thompson5910
Summary: Todd spent $75 Matt spent $50 Jeff spent $150
jim_thompson5910
  • jim_thompson5910
not sure how you got $45
anonymous
  • anonymous
damn girllllll..... you shouldnt be talking to this loser you should kik me ;)
anonymous
  • anonymous
i thought matt's equation was m-25,
jim_thompson5910
  • jim_thompson5910
SwoleNerd this is a study site, not facebook
anonymous
  • anonymous
and i dont have kik.
anonymous
  • anonymous
lol girl how old are you im 15
anonymous
  • anonymous
ok jim i have another question.
jim_thompson5910
  • jim_thompson5910
Matt's equation is M = T - 25
jim_thompson5910
  • jim_thompson5910
replace T with 75 (remember we found that T = 75) and you'll get M = 50
anonymous
  • anonymous
ok i got it.
anonymous
  • anonymous
god bless!
jim_thompson5910
  • jim_thompson5910
what's your other question?
anonymous
  • anonymous
its really long so hold on.
jim_thompson5910
  • jim_thompson5910
alright
anonymous
  • 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
  • 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
  • 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
  • anonymous
hello
jim_thompson5910
  • jim_thompson5910
sorry still reading and thinking
jim_thompson5910
  • 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
  • jim_thompson5910
"Macy scored 4 times as many goals as Erin." means Ma = 4*E
jim_thompson5910
  • jim_thompson5910
"Carly scored 2 goals less than Macy." means C = Ma - 2
jim_thompson5910
  • jim_thompson5910
"Shelly scored one half as many goals as carly." means S = C/2
jim_thompson5910
  • jim_thompson5910
"Molly scored 1 more goal than Macy." means Mo = Ma + 1
jim_thompson5910
  • 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
  • jim_thompson5910
because Ma = 4*E, we can solve for E to get E = Ma/4
jim_thompson5910
  • 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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