Question 1069023: A group of twenty-five coins, whose total value is $2.75, is composed of nickels, dimes, and quarters. If the nickels were dimes, the dimes were quarters, and the quarters were nickels, the total would be
$3.75. How many quarters are there in the collection?
Found 2 solutions by ikleyn, ankor@dixie-net.com:
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Let n = #nickels, d = #dimes, q = #quarters.
Then your equations are
n + d + q = 25, (1)
5n + 10d + 25q = 275 (2) (cents)
10n + 25d + 5q = 375. (3)
To solve it, express n = 25 - d - q from (1), then substitute it into (2) and (3), replacing n in each of these two equations. You will get
5*(25 - d - q) + 10d + 25q = 275 (2')
10*(25 - d - q) + 25d + 5q = 375. (3').
Simplify to get the standard form of a 2x2 system.
Then solve it by any method you know to get n = 10, d = 10 and q = 5.
It is just technique.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! Write an equation for each phrase/statement
:
A group of twenty-five coins, composed of nickels, dimes, and quarters.
n + d + q = 25
:
whose total value is $2.75,
.05n + .10d + .25q = 2.75
:
If the nickels were dimes, the dimes were quarters, and the quarters were nickels, the total would be $3.75.
.10n + .25d + .05q = 3.75
:
using the matrix feature on your calc,enter
1, 1, 1, 25
.05 .1 .25 2.75
.1 .25 .05 3.75
you get: 10 nickels, 10 dimes, 5 quarters
How many quarters are there in the collection?
|
|
|
