Algebra word problem help?
I cannot figure out this problem. My algebra teacher said that we are only allowed to use on variable. I need: an equation, the answer, and step by step instructions.
Sarah has ten times as much money as Danielle. Sarah also has thirty times as much money as Rebecca. Together they have a total of $170. How much money does each person have?
Update:We can only use ONE variable
Comments
Let S represent Sarah's $$$
Let D represent Danielle's $$$
Let R represent Rebecca's $$$
I'll change to one variable later
Given:
S=10D because of the first line. S= 10 times D
S=30R because of the second line. S = 30 times R
S+D+R=170 because of the last line. together
What is the relationship between D and R?
Well, 10 D must equals to 30 R, because they both equal to S
10D = 30R....divide both side by 10
D = 3R
So now S = 30R...D=3R....and R = R (NOW, you have one variable.)
So S + D + R = 170....substitute with R
30R + 3R + R = 170...Collect terms
34R = 170...Divide both side by 34
R = 5
Recollect that D = 3R; 3 x 5 = 15.
Recollect that S = 30R; 30 x 5 = 150
Therefore, Sarah has $150, Danielle has $15, and Rebecca has $5.
Let Sarah=S
Let Danielle=D
Let Rebecca=R
S+D+R=170
Sarah has ten times as much money as Danielle
S=10D
S/10=D
Sarah has thirty times as much as Rebecca
S=30R
S/30=R
If D=S/10 and R=S/30, substitute these in for your variables
S+D+R=170
S+(S/10)+(S/30)=170
Solve for S
30S+3S+S=5100
34S=5100
S=150
D=S/10
150/10=D
15=D
S/30=R
150/30=R
5=R
Sarah=150
Danielle=15
Rebecca=5
You ARE using only one variable. You have to convert the other two into the one to figure out the problem.
S+(S/10)+(S/30)=170
Danielle's money equals x
Sarah's money then equals 10x
Rebecca's money equals (1/3)x (being that she has 30 times less money than Sarah who's money is 10x)
Therefore, x + 10x + (1/3)x =170
Combine x variables into one equation and solve for x. Then insert into values above.
Sarah = 150
Danielle = 15
Rebecca = 5