SOLUTION: Lydia, Sarah, and Denise collected campain buttons. Lydia had 20 more buttons than Sarah. Denise had 3 times as many buttons as Sarah. If the total number of campaign buttons the

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Question 283717: Lydia, Sarah, and Denise collected campain buttons. Lydia had 20 more buttons than Sarah. Denise had 3 times as many buttons as Sarah. If the total number of campaign buttons the 3 girls had was 120, how many buttons did Lydia have?
Found 2 solutions by richwmiller, oberobic:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
L+S+D=120
L=S+20
D=3S
D = 60, L = 40, S = 20

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
L = number of buttons collected by Lydia
S = number of buttons collected by Sarah
D = number of buttons collected by Denise
L + S + D = 120 :: Total given.
.
L = S + 20 :: Lydia has 20 more than Sarah
D = 3S :: Denise had 3 times as many as Sarah
.
Question: How many did Lydia have?
.
We have 3 unknowns, so we need 3 equations...
OR
We need to redefine the variables to use fewer than 3 unknowns.
.
Looking back, the problem was stated in terms of Sarah's buttons.
.
L = S+20
D = 3S
and
S = S of course
.
L + D + S = 120 :: given
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substituting...
.
(S+20) + 3S + S = 120
5S = 100
S = 20
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Substituting this value
.
L = S + 20
L = 20 + 20 = 40
.
D = 3S
D = 3(20) = 60
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Checking, does L+S+D = 120?
20 + 40 +60 = 120
Yes!
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Rechecking the question, it only asks how many Lydia has.
.
Answer:
Lydia has 40 buttons.
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Done.