Sue has two more nickels than dimes and three more quarters than nickels. she has $3.35 in all. how many coins of each kind does she have?

can someone give me a step-by-step on how to do
100 points to brainliest!

She has 10 quarters, 5 dimes & 7 nickles.

Step-by-step explanation:

Use N: Nickle, D: Dime, and Q: Quarter. / $3.35 can be expressed as 335 cents in this case

Use what we know for some equations:

N = D+2 since two more nickles than dimes

Q = N+3 since three more quarters than nickles.

Basic Equation: 10D + 5N + 25Q = 335

Substitution Equation: Q= (d+5) + 3 = D+5

Substitution: 5*(d+2)+10D+25*(d+5) = 335

Solve:

5d+10+10d+25d+125 = 335

(Collect the terms)

5d+10d+25d= 40d

10+125= 135

40d + 135 = 335

(Subtract 135 on both sides)

335 - 135 = 200

(What's left)

40D = 200

(Divide)

40/200 = 5

(So,)

D = 5

Therefore there are 5 Dimes

Let's use the two equations up top:

Nickles) N = D+2 / N = 5 + 2 = 7, Therefore 7 nickles

Quarters: Q = N + 3 / Q = 7 + 3 = 10 Quarters

You can add them together if you'd like to check.

10Q = $2.50

5D = $.50

7N = $.35

(Add them up)

2.50+.50+.35 = $3.35!

Number of nickels: n

Number of dimes: d

Number of quarters: q  

Given:

n=d+2 , two more nickels than dimes,  

q=n+3, three more quarters than nickels

Value of n nickels is 5n cents

Value of d dimes is 10d cents

Value of q quarters is 25q cents  

Total money is $3.35 which can also be expressed as 335 cents.  

5n+10d+25q=335

since n=d+2 and q=n+3, by substitution we can say that q=(d+2)+3=d+5

Now take the value equation and substitute the two expressions for nickels and quarters in terms of dimes in place of the n and q variables:  

5(d+2)+10d+25(d+5)=335

Distribute and collect terms:

5d+10+10d+25d+125

40d+135=335

Add -135 to both sides:

40d=200  

Divide by 40:

d=5  

so there are 5 dimes. that means that there are 5+2=7 nickels and 5+5=10 quarters.

Check the

10 quarters is $2.50,

5 dimes is $.50,

7 nickels is $.35, and finally,

$2.50 plus $.50 plus $.35 = $3.35

~Hope this helps!!

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