20 coins, consisting of dimes and quarters.
if the values were switched, the difference would be 90 cents.
This is how i came up with my answer.
solving the system:
one equation describes the number of coins: x + y = 20
where x is the number of dimes and y is the number of quarters.
the other equation describes the amount of money:
(0.25x + 0.1y) - (0.1x + 0.25y) = 0.90
(0.25x + 0.1y) describes when the dimes are quarters and the quarters are dimes.
(0.1x + 0.25y) describes when the dimes and quarters are their original values.
The difference is supposed to be $0.90 or 90cents.
Therefore,
by the elimination method of solving a system of equations:
x + y = 20 #1
(0.25x + 0.1y) - (0.1x + 0.25y) = 0.9 #2
simplify #2 to become:
0.15x - 0.15y = 0.9 #3
x + y = 20 #1
0.15x - 0.15y = 0.9 #3
multiply #1 by 0.15:
0.15x + 0.15y = 3 #4
0.15x - 0.15y = 0.9 #3
add #4 and #3:
0.30x = 3.9
x = 13
therefore, the number of dimes that the man has is 13.
to find the number of quarters, x is evaluated in the 1st equation.
x + y = 20
13 + y = 20
y = 20 - 13
y = 7
This can be checked as follows.
13 dimes = 130 cents
7 quarters = 175 cents
total = 305 cents
13 quarters = 325 cents
7 dimes = 70 cents
total = 395 cents
The difference between the two is 90 cents.
Therefore, the man had 13 dimes and 7 quarters.
By the way, is this a question that you are doing in class, have the answer to and are seeing who can figure it out, or are you proposing it for another reason?
Addendum (by PatrickLMT): Actually, this question was featured in the February 26, 1974 comic strip "Peanuts." Peppermint Patty had this question in school and despaired of finding the answer.
10 quarters = 250 cents (25 x 10) 7 dimes = 70 cents (7 x 10) 250 + 70 = 320 10 quarters and 7 dimes equal 320 cents. In other words, $3.20 or 3 dollars and twenty cents.
1 quarter = 25 x (1) cents 2 quarters = 25 x (2) cents 3 quarters = 25 x (3) cents 4 quarters = 25 x (4) cents . . . 'q' quarters = 25 x (q) cents
4 quarters = 1 dollar = 100 cents
2 quarters would be 50 cents, since 1 quarter is 25 cents.
1 quarter = 25 cents 1 dime = 10 cents ⇒ 10 quarters + 2 dimes = 10 x 25 cents + 2 x 10 cents = 270 cents
one dollar & ninety cents
two-hundred ninety-six dollars and seventy-six cents
$29.99 is spelled like this: twenty nine dollars and ninety nine cents. 29.99 as a whole number and decimal would be: twenty nine point ninety nine or twenty nine and ninety nine hundredths.
you have 375 cents in quarters and give away 14 of them :)
The number 427.90 is "four hundred twenty-seven and ninety hundredths." In US currency, the value $427.90 is "four hundred twenty-seven dollars and ninety cents."
Like this: $3,427.90
2 quarters,4 dimes, and 3 pennies
The number is twenty-eight thousand four hundred ninety-nine and ninety-four hundredths. It would ordinarily be spoken as "twenty-eight thousand four hundred ninety-nine point nine four." The currency value $28,499.94 is "twenty-eight thousand four hundred ninety-nine dollars and ninety-four cents."
four thousand, five hundred and ninety-eight dollars and twenty-six cents
I would write it as three hundred ninety four point two seven. Or three hundred ninety-four and twenty-seven hundredths. The US currency value $394.27 is three hundred ninety-four dollars and twenty-seven cents.
10 quarters = 250 cents (25 x 10) 7 dimes = 70 cents (7 x 10) 250 + 70 = 320 10 quarters and 7 dimes equal 320 cents. In other words, $3.20 or 3 dollars and twenty cents.
three hundred and ninety-three dollars and twenty-four cents in USA currency for example