Pls answer in detail. A jar of dimes & quarters contains $15.25. There are 103 coins in all. How many each?

Question

Pls answer in detail. A jar of dimes & quarters contains $15.25. There are 103 coins in all. How many each?

Answer 1

let number of dimes be n and number of quarters be m.

10n + 25m = 1525 => 2n + 5m = 305

m + n = 103 => n = 103 - m

2(103 - m) + 5m = 305

=> 206 - 2m + 5m = 305

=> 3m = 99

=> m =33

=> n = 70

Answer 2

There are 33 Quarters:  33x.25 = $8.25

There are 70 Dimes:  70 x .10 = $7.00

Total $15.25

Answer 3

Let there be x quarters and y dimes

Each quarter is worth 25 cents

Each dime is worrh 10 cents

x+y=103

25x+10y=1525 (convert all to cents)

y=103-x

25x+10(103-x)=1525

25x+1030-10x=1525

15x=1525-1030

15x=495

x=33

y=103-33=70

There are 25 quarters and 70 dimes.

  

Answer 4

d+q=103

.10d+.25q=15.25

d=103-q

.10(103-q)+.25q=15.25

10.30-.10q+.25q=15.25

15q+10.30-10.30=15.25-10.30

.15q=4.95

q= 4.95/.15

q=33 d=70

33*.25= 8.25

70*.10=7.00

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

103 c0ins totaling 15.25

Answer 5

Let

D = number of dimes in the jar

Q = number of quarters in the jar

Equation 1 -- A jar of dimes & quarters contains $15.25.

0.10D + 0.25Q = 15.25

Equation 2 -- << There are 103 coins in all. >>

D + Q = 103

<< How many each? >>

From Equation 2, D = 103 - Q and substituting this in Equation 1,

0.10(103 - Q) + 0.25Q = 15.25

10.3 - 0.1Q + 0.25Q = 15.25

0.15Q = 4.95

Q = 33

Solving for "D"

D = 103 - 33 = 70

ANSWER:

Number of quarters = 33

Number of dimes = 70

CHECK:

0.10(70) + 0.25(33) = 15.25  

Answer 6

d = number of dimes

q = number of quarters

d + q = 103

0.10d + 0.25q = 15.25

Use elimination to solve the system of equations:

Multiply the first equation by -0.10 and add to the second equation:

   -0.10d - .10q = -10.3

+ 0.10d + 0.25q = 15.25

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

0.15q = 4.95

q = 33

Then, substitute q in the first equation to find d:

d + 33 = 103

d = 70

Therefore,

q = 33, d= 70

Answer 7

So...let "d" be the number of dimes, and "q" be the number of quarters.

d + q = 103 (number of dimes + number of quarters = 103 coins)

10d + 25q = 1525  (each dime is worth 10 cents, each quarter is worth 25 cents, and the total = 1525 cents)

That's just a simple "two equations with two unknowns", which I'm sure you can figure out by yourself.

Answer 8

Got it! 70 dimes x .1= 7.00 + 33 quarters x .25= 8.75, therefore, 70 dimes + 33 quarters= 103 coins. 7.00 dollars + 8.75 dollars= 15.25!  

Answer 9

70 Dimes

33 Quaters!

Answer 10

you need 2 equations to solve this.

D+Q=103

.1D+.25Q=15.25

now solve for D to get D=103-Q

substitute D into the 2nd equation

.1(103-Q) +.25Q=15.25

10.3-.1Q+.25Q=15.25

Now it's your turn... finish solving for Q and that's the number of quarters.  Plug that into the first equation and solve for D to get the number of dimes.