Math Question

[paymaant]

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Anne has a total of $34 in nickels, dimes, and quarters. If she has 3 times as many dimes as quarters and 2 times as many nickels as dimes, how many dimes does she have?

The answer is 120 ! How would you go about solving this problem? Thanks!

 

[J777]

Let N= number nickels, D = number of dimes, and Q = number of quarters
We know that the total monetary value is $34. Since one nickel is worth 0.05 dollars, we must multiply the number of nickels by 0.05. Since one dime is worth 0.1 dollars..... This gives us our main equation:

(1) 0.05N + 0.1D + 0.25Q = 34

Also, to reflect the relationships between the different coins:

(2) Q = (D/3)
(3) N = 2D

In order to accurately reflect the relationship between dimes and quarters, we must say (D/3) = Q. When we divide the number of dimes by three, this will give us the amount of quarters present.

Same for nickels and dimes.. since there are 2 times as many nickels as dimes, when we multiply the number of dimes by two, we get the number of nickels: N = 2D

Now, simply plug equations (2) and (3) into equation (1) and you will get 120. Make sure that everything is in terms of D because the question asks for the number of dimes:

0.05(2D) + 0.1D + 0.25(D/3) = 34 (I will convert to fractions because this will be easier)
(1/10)D + (1/10)D + (1/12)D = 34
(1/5)D + (1/12)D = 34
(17/60)D = 34 (notice that 34/17 = 2 and 2 times 60 = 120)
D = 120

 

[gn4]

let me see if I can help. I will let X be the number of dimes. If you do this, you have X amount of dimes, + X/3 amount of quarters, + 2X amount of nickels. All that has to equal $34. Now you need to assign value to the coins. A dime is worth 10 cents, a quarter is worth 25 cents, and a nickel is worth 5 cents.

10X dimes

25X/3 quarters

2X(5) nickels

10x + 25x/3 + 10x = 3400cents($34)

solve for X and I get 120.

Somebody correct me if I did that wrong.

 

[gn4]

Let N= number nickels, D = number of dimes, and Q = number of quarters
We know that the total monetary value is $34. Since one nickel is worth 0.05 dollars, we must multiply the number of nickels by 0.05. Since one dime is worth 0.1 dollars..... This gives us our main equation:

(1) 0.05N + 0.1D + 0.25Q = 34

Also, to reflect the relationships between the different coins:

(2) Q = (D/3)
(3) N = 2D

In order to accurately reflect the relationship between dimes and quarters, we must say (D/3) = Q. When we divide the number of dimes by three, this will give us the amount of quarters present.

Same for nickels and dimes.. since there are 2 times as many nickels as dimes, when we multiply the number of dimes by two, we get the number of nickels: N = 2D

Now, simply plug equations (2) and (3) into equation (1) and you will get 120. Make sure that everything is in terms of D because the question asks for the number of dimes:

0.05(2D) + 0.1D + 0.25(D/3) = 34 (I will convert to fractions because this will be easier)
(1/10)D + (1/10)D + (1/12)D = 34
(1/5)D + (1/12)D = 34
(17/60)D = 34 (notice that 34/17 = 2 and 2 times 60 = 120)
D = 120

or you can do it this way too. haha

 

[J777]

or you can do it this way too. haha

Ha! Definitely go with gn's method. Faster, more concise, easier numbers

 

[paymaant]

thanks guys! I understand it now

 

[trocha86]

Why is it 25x/3 ? I thought it would be D=1Q/3 Im not understanding how you got that?

 

[gn4]

Why is it 25x/3 ? I thought it would be D=1Q/3 Im not understanding how you got that?

Q= D/3 is what you should have because you have 3 times as many dimes as quarters.

Because a quarter is worth 25cents, then you take that into account as well.

Q=25(D/3)

 

[aznnytezx]

Try this, I haven't started math destroyers.. So idunno any methods.
Let X be the quarters amount, and the numbers be the values.

.25X +.30X +.30X = 34

You have .85X = 34

X= 40

Quarters x 3 = 120. Done.