SOLUTION: An old jar of dimes and quarters contains 200 coins total, and the value of all the coins is $42.50. How many quarters are in the jar? A. 50 B. 130 C. 127 D. 150

Question 1127664: An old jar of dimes and quarters contains 200 coins total, and the value of all the coins is $42.50. How many quarters are in the jar?
A. 50
B. 130
C. 127
D. 150
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
An old jar of dimes and quarters contains 200 coins total, and the value of all the coins is $42.50. How many quarters are in the jar?
============
d + q = 200
10d + 25q = 4250
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The age of the jar is not relevant.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let's finish solving the problem using formal algebra, with the way the other tutor gets you started. Then let's look at how you can get the answer without the formal algebra, using the exact same calculations, using logical reasoning. If you are good at mental arithmetic, you will reach the answer much faster than with the formal algebra.

(1) q+d = 200 [there are 200 coins, quarters and dimes together]
(2) 25q+10d = 4250 [the total value of the coins is $42.50 = 4250 cents]

Multiply the first equation by 10:

(3) 10q+10d = 2000

Subtract (3) from (2), eliminating d, then solve for q:

15q = 2250
q = 2250/15 = 150

ANSWER: the number of quarters in the jar is 150.

Now let's see how we can get that answer without the formal algebra, through logical reasoning.

(1) If all 200 coins were dimes, the total value would be $20.00 = 2000 cents.
(2) the actual total value, $42.50 = 4250 cents, is 2250 cents more than that.

Now think of replacing dimes with quarters, keeping the total number of coins the same, to make the total value of the coins $42.50. Each time we replace a dime with a quarter, the total value increases by 25-10 = 15 cents.

(3) The difference between the value of a quarter and a dime is 15 cents; the number of quarters needed to make up the additional 2250 cents is 2250/15 = 150.

Same answer, using the exact same calculations; but without the need for pencil and paper and algebra.
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