SOLUTION: Sam found a number of nickels, dimes and quarters. He found 3 more dimes than nickels but twice as many quarter as dimes. The total value of the coins was $5.05. How many coins of
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-> SOLUTION: Sam found a number of nickels, dimes and quarters. He found 3 more dimes than nickels but twice as many quarter as dimes. The total value of the coins was $5.05. How many coins of
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Question 160600: Sam found a number of nickels, dimes and quarters. He found 3 more dimes than nickels but twice as many quarter as dimes. The total value of the coins was $5.05. How many coins of each type did Sam find? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Sam found a number of nickels, dimes and quarters. He found 3 more dimes than
nickels but twice as many quarter as dimes. The total value of the coins was
$5.05. How many coins of each type did Sam find?
;
Let:
n = no. of nickels
d = no. of dime
q = no. of quarters
:
Write an equation for each statement:
;
"He found 3 more dimes than nickels"
d = 3+n
or
n = (d-3)
:
" but twice as many quarter as dimes."
q = 2d
:
"The total value of the coins was $5.05."
.05n + 10d + .25q = 5.05
:
How many coins of each type did Sam find?
:
Substitute for q and n in the total$ equation
.05(d-3) + .10d + .25(2d) = 5.05
.05d - .15 + .10d + .50d = 5.05
.05d + .10d + .50d = 5.05 + .15
.65d = 5.20
d =
d = 8 dimes
then
n = 8 - 3
n = 5 nickels
and
q = 2*8
q = 16 quarter
:
8 + 5 + 16 = 29 coins total
;
:
Check solution in the total$ equation
.05(5) + .10(8) + .25(16) =
.25 + .80 + 4.00 = 5.05; confirms our solutions
