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A collection of nickels dimes and quarters amount to $10.00 there are 140 coins and there is twice as many dimes as quarters, find the number of nickels
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Your equations are
n + d + q = 140, (1)
5n + 10d + 25q = 1000, (2)
d = 2q. (3)
(three equations in 3 unknowns). Substitute (3) into (1) and (2).
In this way you eliminate d and reduce the system to 2 equations in 2 unknowns:
n + 2q + q = 140, (4) (instead of (1))
5n + 10*2q + 25q = 1000. (5) (instead of (2))
Now simplify equations (4) and (5)
n + 3q = 140, (6)
5n + 45q = 1000. (7)
Next express n = 140 - 3q from (6) and substitute it into (7). You will get a single equation for q
5*(140-3q) + 45q = 1000. (8)
Simplify (8)
700 - 15q + 45q = 1000,
30q = 1000-700 = 300,
q = = 10.
Now n = 140 - 3q = 140 - 3*10 = 140 - 30 = 110, and
d = 2q = 2*10 = 20.
Answer. n = 110, d = 20 and q = 10.