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

Sign In or Register to comment.