SOLUTION: The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters the total value of the coins would be $7.80. a) set up a s

Question 1132844: The total value of quarters and dimes in a coin bank is $6.90.
If the quarters were dimes and the dimes were quarters the total value of the coins would be $7.80.
a) set up a system of equations to represent the situation.
b) find the number of quarters in the bank.
Found 3 solutions by josmiceli, ikleyn, Alan3354:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the number of dimes
Let = number of quarters
-----------------------------------------
(1) ( in cents )
(2) ( in cents )
---------------------------------------------
Multiply both sides of (1) by
Multiply both sides of (2) by
Subtract (2) from (1)
(1)
(2)
--------------------------------------

and
(1)
(1)
(1)
(1)
-----------------------
There are 24 dimes and 18 quarters
--------------------------------------------
check:
(2)
(2)
(2)
(2)
OK
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.

The system of equations is 10x + 25y = 690 cents (1) (x = # of dimes; y = # of quarters) 25x + 10y = 780 cents (2) To solve the system, multiply equation (1) by 5 (both sides) and multiply equation (2) by 2. You will get 50x + 125y = 5*690 (3) 50x + 20y = 2*780 (4) Now subtract eq(4) from eq(3). The terms "50x" will cancel each other, so you eliminate the unknown "x" and get a single equation for the unknown y in this way (it is how the Elimination method works) 125y - 20y = 5*690 - 2*780 105y = 1890 ==============> y = = 18. ANSWER. The number of quarters in the bank is 18.

Solved.

-------------------

On the way, you learned from my post on how the Elimination method works.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The total value of quarters and dimes in a coin bank is $6.90.
If the quarters were dimes and the dimes were quarters the total value of the coins would be $7.80.
------------------------
25q + 10d = 690
---------
Each swap of a dime for a quarter adds 15 cents.
780 - 690 = 90
90/15 = 6 swaps, which is the difference between the # of d's and q's
Since the total increases, d > q
----
d - q = 6
---
10d + 25q = 690 --> 5q + 2d = 138
2d + 5q = 138
2d - 2q = 12
-------------------- Subtract
7q = 126
q = 18 quarters
d = 24 dimes
RELATED QUESTIONS
The total value of the quarters and dimes in a coin bank is $5.20. If the quarters were... (answered by lwsshak3)
A coin bank contains dimes and quarters. The total value of the coins is $10.40. If the... (answered by stanbon)
The total value of the nickels, dimes, and quarters in a coin bank is $4. If the nickels... (answered by stanbon)
question #16 the total value of the dimes and quarters in a coin bank is $3.70. if the (answered by drj)
A coin bank contains only dimes and quarters. The ToTal value of The coins in The bank is (answered by mananth)
The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes (answered by josgarithmetic)
The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes (answered by Theo,josgarithmetic)
The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes (answered by josmiceli,josgarithmetic)
The total value of the quarters and dimes in a coin bank is $8.00. If the quarters were... (answered by drj)