how many quarters does warren have

Question

Warren has 40 coins (all nickels, dimes and quarters) worth $4.05. he has 7 more nickels than dimes. How many quarters does Warren have?

Answer 1

let's Warren has x quarters, y dimes, and y+7 nickels

therefore, x+y+y+7=40

=> x+2y +7 =33 +7 ..... by adjusting operators

=> x+2y=33 .................by subtracting 7 from both sides .... (1)

25x+10y+5(y+7)=405

=>5x+2y+y+7=81 ... Dividing both sides by 5

=>5x +3y+7=81 ...... By adjusting operators

=>5x +3y=74 .................by subtracting 7 from both sides .... (2)

multiplying (1) by 5,  5x+10y=165

 

                 from (2)  5x +3y = 74

Subtracting,                    7y=   91

=>                                  y =   13 ... Dividing both sides by 7

Substituting y=7 in (1), x+26=33

=>                              x     =7

Hence Warren has 7 quarters.

 

Proof: 7 quarters make $1.75; 13 dimes make $1.30; (13+7)=20 nickel make $1, all of them together make $4.05.

Answer 2

Let X = the number of  dimes.

 

Then X + 7 = the number of nickels

 

Let Y = the number of quarters

 

So we have two variables.  That means that we need two equations to solve.

 

First, we know that the total number of coins = 40. 

 

So X + X + 7 + y = 40

 

Combining like terms--> 2X +7 + y = 40

 

Solving for y --> y = 40 - 2X - 7

 

y = 33 - 2X

 

Second, the value of all coins = $4.05 which is 405 cents, so we won't have to work with decimals.

 

The value of dimes = 10X cents (there are 10 cents in a dime)

 

The value of nickels = 5(X + 7) = 5X + 35   (there are 5 cents in a nickel

 

The value of quarters = 25y  (there are 25 cents in a quarter

 

So the total value equals the sum of all three individual values:  405 = 10X + 5X + 35 + 25y

 

Substitute 33 - 2X for y in this equation --> 405 = 10X + 5X +35 + 25(33 - 2x)

 

405 = 15X + 35 + 825 - 50X

 

405 = -35X + 860

 

-455 = -35X

 

X = 13 which is the number of dimes. But the question asks for the number of quarters which is y

 

y = 33 -2x

 

y = 33 - 2(13)

 

y = 33 - 26

 

y = 7 <-- Answer!

 

Figure out the number of nickels and then check the answers by making sure that the total number of coins is 40 and the total value is 405 cents.  I could have made a mistake so you want to check up on me and make sure that I'm correct.

Answer 3

let x = # of dimes

# of nickels = x+7

y = # of quarters

1) x + x + 7 + y = 40 = total # of coins = 2x + 7 + y

2) 10x +5(x+7) + 25y = 405 = total money = 15x + 35 + 25y

 

two equations with two unknons can be solved several different ways

rearrange first equation to solve for y = 33 - 2x

substitute into second equation to get rid of y

405 = 15x + 35 + 25(33-2x) = 15x + 35 + 825 - 50x

405 - 860 = -35x = -455

x = 13

number of nickels = x + 7 = 20

number of quarters = y = 33 - 2x = 7

 

 

 

 

Answer 4

n = nickels

d = dimes

q = quarters

 

3 variables generally means you will need to set up 3 equations

 

n + d + q = 40 (number of coins)

d + 7 = n (7 more nickels than the number of dimes)

$0.05n + 0.10d + 0.25q = $4.05 (monetary value)

 

I like to start with the variable that is 'defined' (n = d+7)**********

Plug d + 7 into the first equation, you will get (d+7) + d + q = 40.

Combine 'like terms' to get 2d + q + 7 = 40

=> 2d + q = 33

=> 2d = 33 - q

=> d = (33 - q)/2 ************

(Strategy is to find "d". You will see why during the next step.)

 

Plug d + 7 into the 3rd equation to get:

=> 0.05(d+7) + 0.10d + 0.25q = $4.05

=>0.05d + 0.35 + 0.10d + 0.25q = $4.05

=> 0.15d + 0.25q = $3.70 ************

You found "d" above, so now plug "d" into the monetary expression, and solve for q.