Quarters, Nickels and Dimes question?

Question

Numeric Response:
Use a system of equations to solve a problem involving coins.

Ryan has $21.40 in dimes and quarters. He has 103 coins in all. How many of each type of coin does he have?

Answer 1

When dealing with money problems such as this one, there is always going to be 2 equations.

First equation:
# of dimes + # of quarters = Total # of coins

Second equation:
Value of dimes + Value of quarters = Total value of coins

For now:
Lets call the # of dimes = D
Lets call the # of quarters = Q
Ryan has 103 coins in total

So, plug it in the first equation.

D + Q = 103

Now, we have two choices here. We can rearrange this equation to D = 103 - Q or Q = 103 - D It doesn't matter. Lets use Q = 103 - D

Now we have:

# of dimes: D
# of quarters: Q = 103 - D

The first equation is complete. Let's look at the second equation now:

Value of dimes + Value of quarters = Total value of coins

When I say "value" of dimes it means how much money in dimes there are. For example, if I had 5 dimes, how much money do I have? That's right, 50 cents. How did you get that? You went 5 x 10. That means that the value of dimes Ryan has is 10 x D or 10D.

So therefore:
Value of dimes = 10D
Value of quarters = 25( 103 - D )
Total value of coins = 2140

Now plug it in the equation:

10D + 25( 103 - D ) = 2140
10D + 2575 - 25D = 2140
-15D = -435
D = 29

Therefore Quarters = 103 - 29
Q = 74

Sentence answer:
Ryan has a total of 29 dimes and 74 quarters.


*Note: The reason why I used 2140 in the equation instead of 21.40 is because a dime is actually 0.10 and a quarter is actually 0.25 so I moved the decimal place by 2. If I move the decimal place by 2 then I get: 2140, D= 10, Q = 25

Answer 2

If D equals the number of dimes and Q equals the number of quarters, we know the following:

D + Q = 103.
.10D + .25Q = 21.40.

We can multiply the top equation by -10 and the bottom equation by 100 to get the following:

-10D - 10Q = -1030.
10D + 25Q = 2140.
----------------------------
15Q = 1110.
Q = 74.

And as a result, D + 74 = 103, or D = 29.

And to check: (.10 * 29) + (.25 * 74) = $2.90 + 18.50 = $21.40.

So as a result, Ryan has 29 dimes and 74 quarters.

Answer 3

Hello,

Let d = number of dimes
Let q = number of quarters

so 10d + 25q = 2140
and d + q = 103

so d = 103 - q or 10(103 - q) + 25q = 2140 so we have

1030 - 10q + 25q = 2140 and 1030 + 15q = 2140 so 15q = 1110 pr q = 74 so d = 103 -74 = 29

Hope This Helps!!

Answer 4

You can have a two variable or one variable approach.
For two, let D=dimes and Q=quarters.
D+Q = 103
0.10*D+0.25*Q=21.40

Answer 5

D + Q = 103
Q = 103 - D

0.25Q + 0.10D = 21.4
0.25(103 - D) + 0.10D = 21.4
25.75 - 0.25D + 0.10D = 21.4
-0.15D = -4.35
D = 29
Q = 103 - 29 = 74

Answer 6

I know that he would have 85 quarters then i get stuck lol sorry

Answer 7

.10d + .25q = 21.40
d + q = 103

Solve the system.