algebra word problem?

Question

A jar contains 35 coins consisting of dimes and quarters and having a total value of $4.40. How many of each kind of coin are there?

**i got 29 dimes and 6 quarters but i don't know how to show my work for it. how would i show my work to prove my answer if it is correct?

Answer 1

let d be the number of dimes
let q be the number of quarters

there are 35 coins
d + q = 35

a dime is $.10
a quarter is $.25
.10d + .25q = 4.40

you have two equations
d + q = 35
.10d + .25q = 4.40

-.10(d + q = 35)
.10d + .25q = 4.40

-.10d - .10q = -3.5
.10d + .25q = 4.40
-------------------------
.15q = .9
q = 6

d = 35 - 6
d = 29

Answer 2

You know that the total dimes, d, and quarters, q equals 35 coins: d + q = 35

You also know that the total value is 440 cents:
10*d + 25*q = 440

Multiply the top equation by 10 to get
10d + 10q = 350

Subtract this from the second equation to get
15q = 90
q = 6 quarters
Substitute into the first equation to get
d = 29 dimes

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Hope this all helps.

Answer 3

D = number of dimes
Q = number of quarters

Write out equations for the information given in the problem:
D + Q = 35 and D = 35 - Q .... there are 35 total coins
0.10D + 0.25Q = 4.40 .............. the sum of all coins is 4.40

0.10*(35 - Q) + 0.25Q = 4.40
3.50 + 0.15Q = 4.40
0.15Q = 4.40 - 3.50 = 0.90
Q = 0.90/0.15
So: Q = 6 and D = 35 - Q = 29

If you don't like decimals and it makes it easier for you to use integers then do it using cents:
10D + 25Q = 440

Answer 4

Okay, to get the answer in the first place;

Step 1 : Set up a system of equations;

.1x + .25y = 4.4

x + y = 35

This is essentially what the word problem is saying

Step 2: Solve by any means possible;

10(.1x +.25y = 4.4)

Multiply both sides in order to keep equation equivalent

x + 2.5y = 44

and we add in our other equation in the system

x + y = 35

Now we subtract;

x + 2.5y = 44
-
x + y = 35

1.5y = 9

Divide both sides by 1.5

y = 6

Now we substitute this back into our system

x + 6 = 35

Subtract 6 from both sides

x = 29

Step 3: Check your work;

.1x + .25y = 4.4

.1(29) + .25(6) = 4.4

2.9 + 1.5 = 4.4

4.4 = 4.4

Hope this helps!

: )

Answer 5

x = dimes.
Then .1x + .25(35-x) = 4.40, so .1x + 8.75 - .25x = 4.40, or
.15x = 4.35, and x = dimes = 29. So quarters = 35-29 = 6

Answer 6

35=(.10)d+q(.25) (n=nickles,q=quarters)
35=(.5)(29)+(6)(.25)
35=35