SOLUTION: Moolah has 27 coins that are all dimes and quarters. The value of th coins is $4.35. How many dimes and how many quarters does Moolah have?

Question 161472: Moolah has 27 coins that are all dimes and quarters. The value of th coins is $4.35. How many dimes and how many quarters does Moolah have?
Found 3 solutions by checkley77, Alan3354, nerdybill:
Answer by checkley77(12844)   (Show Source): You can put this solution on YOUR website!
Q+D=27 OR Q=27-D
.25Q+.10D=4.35
.25(27-D)+.10D=4.35
6.75-.25D+.10D=4.35
-.15D=4.35-6.75
-.15D=-2.40
D=-2.40/-.15
D=16 DIMES.
D+16=27
Q=27-16
Q=11 QUARTERS.PROOF:
.25*11+.10*16=4.35
2.75+1.60=4.35
4.35=4.35
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Moolah has 27 coins that are all dimes and quarters. The value of th coins is $4.35. How many dimes and how many quarters does Moolah have?
---------------------
D + Q = 27 (a total of 27 coins)
10D + 25Q = 435 (each dime is 10 cents, each quarter 25 cents. See that?)
-------------
Now it's 2 eqns in 2 variables, no longer a "word problem"
Substitution is the easiest approach.
Since D + Q = 27, D = 27-Q.
Sub for D in the 2nd eqn
10*(27-Q) + 25Q = 435
270 - 10Q + 25Q = 435
270 + 15Q = 435
15Q = 165
Q = 11 (11 quarters)
D = 27-Q
D = 16
That's it.
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Let d = number of dimes
and q = number of quarters
.
From "Moolah has 27 coins" we get equation 1:
d+q = 27
.
From "The value of th coins is $4.35" we get equation 2:
.10d + .25q = 4.35
.
Solving equation 1 for d:
d+q = 27
d = 27-q
.
Substitute the above into equation 2 and solve for q:
.10d + .25q = 4.35
.10(27-q) + .25q = 4.35
2.7 - .10q + .25q = 4.35
.15q = 1.65
q = 11 (number of quarters)
.
Substitute the above back into equation 1 and solve fo d:
d+q = 27
d+11 = 27
d = 16 (number of dimes)

RELATED QUESTIONS
Moolah has 27 coins that are all dimes and quarters. The value of the coins is $4.35. How (answered by checkley77)
Moolah has 27 coins that are all dimes and quarters. The value of the coins is $4.35. How (answered by KMST)
moolah has 24 coins that are all dimes and quarters. the value of the coins is $3.75. how (answered by josmiceli)
solve. moolah has 24 coins that are all dimes and quarters.the value of the coins is... (answered by mananth)
Solution: solve for x and y. Moolah has 27 coins that are all dimes and nickles. The... (answered by JBarnum,TimothyLamb)
Bob has 60 coins of quarters and dimes. The coins combined value is $9.45. Find out how... (answered by ewatrrr)
Cameron has 45 coins, all dimes and quarters. The total value of the coins is $9.15.... (answered by MathTherapy,ikleyn)
bob has 60 coins consisting of quarters and dimes. The coins combined value is $9.45.... (answered by mananth)
Bob has 60 coins consisting of quarters and dimes. The coins combined value is $9.45.... (answered by stanbon)