Question 1177788: there are 60 coins in a jar. Some are quarters and some are dimes. The total value is $12.30. How many of each coin is in the jar? Found 2 solutions by mananth, greenestamps:Answer by mananth(16946) (Show Source):
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let number of quarters be x
and dimes be y.
x+y=60
The total value is $12.30.
25x+10y = 1230 ( in cents)
x + y = 60.00
25 x + 10 y = 1230.00 .............2
Eliminate y
multiply (1)by -10.00
Multiply (2) by 1.00
-10 x -10 y = -600.00
25 x 10 y = 1230.00
Add the two equations
15.00 x = 630.00
/ 15.00
x = 42
plug value of x in (1)
1.00 x + 1.00 y = 60.00
42.00 + 1.00 y = 60.00
1.00 y = 18.00
y = 18.00
Ans x = 42
y = 18
42 quarters
18 dimes
The response from the other tutor shows one formal algebraic solution.
If formal algebra is not required, and the speed of obtaining an answer is important (as in a timed math competition), here is an easy informal way to find the answer to this or any number of similar problems.
(1) Suppose all 60 coins were dimes; the total value would be $6.00; the actual total is $6.30 more than that.
(2) Imagine switching a dime for a quarter; that keeps the total number of coins the same but increases the total value by 15 cents.
(3) The number of times you need to switch a dime for a quarter to make the additional $6.30 = 630 cents is 630/15 = 42.
