SOLUTION: Sarah has a collection of nickels, dimes, and quarters worth $15.75. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she

Question 68149This question is from textbook Algebra for College Students
: Sarah has a collection of nickels, dimes, and quarters worth $15.75. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have? This question is from textbook Algebra for College Students

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement:
:
"Sarah has a collection of nickels, dimes, and quarters worth $15.75."
.05n + .1d + .25q = 15.75
:
"She has 10 more dimes than nickels"
d = n + 10
:
"twice as many quarters as dimes."
q = 2d
:
How many coins of each kind does she have?
:
Take the 2nd equation and arrange it so n is in terms of d also
n + 10 = d
n = (d - 10)
:
In the 1st equation substitute (d-10) for n and 2d for q:
.05n + .1d + .25q = 15.75
:
.05(d-10) + .1d + .25(2d) = 15.75
:
.05d - .5 + .1d + .5d = 15.75
:
.65d - .5 = 15.75
:
.65d = 15.75 + .5
:
.65d = 16.25
:
d = 16.25/.65
:
d = 25 dimes
:
Remember the statement "twice as many quarters as dimes."
q = 2(25)
q = 50 quarters
:
The statement "She has 10 more dimes than nickels"
n = 25 - 10
n - 15 nickels
:
Check our solutions
.05(15) + .1(25) + .25(50) =
.75 + 2.50 + 12.50 = 15.75 proves our solutions
:
How about this? Did it make sense to you??
RELATED QUESTIONS
Sarah has a coin collection of nickels, dimes, and quarters worth $15.75. She has 10 more (answered by josmiceli)

Sarah has a collection of dimes, nickels, and quarters worth $15.75. She has 10 more... (answered by math-vortex)

sarah has a collection of nickels, dimes and quarters worth $12.50. she has 10 more dimes (answered by Alan3354)

Sara has a collection of nickels, dimes, and quarters, worth $15.75. She has 10 more... (answered by stanbon)

Robin has a collection of nickels, dimes, and quarters worth $38.50. She has 10 more... (answered by jorel1380)

Robin has a collection of nickels, dimes, and quarters worth $25.50. She has 10 more... (answered by josgarithmetic)

Robin has a collection of nickels, dimes, and quarters worth $37.50. She has 30 more... (answered by ikleyn,greenestamps,josgarithmetic)

Sara has a collection of nickels, dimes and quarters worth $30.75. she has 15 more dimes... (answered by mananth)

Robin has a collection of nickels, dimes, and quarters worth $50.50. She has 30 more... (answered by jorel555)